Photoemission study of intermetallic superconductors: Boro ...wyvern.phys.s.u-tokyo.ac.jp/f/Research/arch/MasterThesis_K Kobayashi.pdf · Chapter 1 Introduction 1.1 Compounds Studied

Photoemission study of

intermetallic superconductors:

Boro-carbides and Chevrel-phase

compounds

Master Thesis

Kensuke Kobayashi

Department of Physics, University of Tokyo

January, 1996

Abstract

We have studied the electronic structures of Ni borかcarbidesLnNi2B2C (Ln = Y

and La) and Chevrel-phase compounds SnxMo6Se7.5 (x = 0 and 1.2) by means of

photoemission and inverse-photoemission spectroscopy.

As to the borかcarbides，the core-level and valence-band spectra of superconducもing

YNi2B2C and non-superconducting LaNi2B2C are presented and are compared with

band-structure calculations. The Ni core-level spectra show weak but distinct satellites

due to twか holebound states， indicating electron correlation within出eNi 3d band.

A1though the gross electronic structure of both compounds is in agreement with the

band-structure calculations except for the twか holebound-state satellites， spectra near

the Fermi level (EF) are quite different from those predicもedby the calculations. That

is， high-resolution photoemission spectra do not show a peak at EF for YNi2B2C and

that at "，0.1 eV below EF for LaNi2B2C， which have been predicted by the calculations，

indicating that electron correlation and/or electron-phonon interaction may play a sig-

nificant role in the low-energy excitations in the Ni borかcarbides.A similar behavior

in the spectra of A15-type superconductors is also poinもedout.

Study on the Chevrel-phase compounds has been performed in almost the same

way. The core-level spectra have revealed systematic core-level shifts between Mo6Se7.5

and Sn1.2Mo6Se7.5 of which the change of the Mか Mointercluster distances seems to be

responsible. It was found that the valence-band spectra have the same tendency unlike

ぬerigid-band model， from which we can propose that the Mo6Ses clusters become

more separated by the intercalation of Sn， which resu1ts in the narrowing of the Mo

4d bands. The valence-band photoemission spectra shows rich fine structures. We will

also reporもthequalitative comparisoIl between the experiment and the band-structure

calculations and large discrepancies especially for the Mo 4d.

In addition， in order to explain the discrepancies between the photoemission spec-

tra and the band-structure calculatioIls， we have studied， using a simple model， the

influence oIi the spectra of the electron-phonoIl interaction， which is supposed to play

a significant role in the spectra near EF. It is reported that realistic parameters mighも

explain the disappearance of the sharp peak at EF of YNi2B2C.

Contents

1 Introduction 1

1.1 Compounds Studied

-BorcトCarbides& Chevrel-Phase Compounds

1.2 Photoemission Spectroscopy 3

References . 9

2 Photoemission Study of Ni Boro・Carbides 11

2.1 Overview. 11

2.1.1 Physical Properties of 8oro-carbides 11

2.1.2 Motivation . 13

2.2 Experiment 18

2.2;1 Sample PreparatioIl . . . . . . 18

2.2.2 Photoemission Measurement . 18

2.3 Resu1ts and Discussions -ー・・・ 19

2.3.1 Core Levels 19

2.3.2 Valence-8and Photoemission Spectra 24

2.3.3 Resonance-Photoemission Spectra of YNi282C . 30

2.3.4 8IS Spectra . 33

2.3.5 Comparison with 8and-Structure Calculations . 35

2.4 Conclusion . 42

References . . . 45

3 Photoemission Study of Chevrel-Phase Compounds 49

3.1 Overview. . 49

3.1.1 Physical Properties of Chevrel-Phase Compounds 49

3.1.2 Motivation . 54

11

3.2 Experiment

3.2.1 Sample Preparation. .

3.2.2 Photoemission Measurement .

3.3 Resu1ts and Discussions

3.3.1 Core Levels

3.3.2 Valence-Band Photoemission Spectra

3.3.3 BIS Spectra . .

3.3.4 Comparison with Band-Structure Calculations

3.4 Conclusion.

References . .

4 Electron-Phonon Interaction and Photoemission Spectra

4.1 Motivation....

4.2 Basis of Model Calculations

4.2.1 Electron-Phonon Interaction in Metal .

4.2.2 Engelsberg&Schrie宜'er'sTheory

4.2.3 Method of Calculations .

4.3 Resulもsand Discussions

4.4 Conclusion.

Rβferences . .

A Engelsberg&Schrieffer's Theory

Acknowledgments

CONTENTS

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Chapter 1

Introduction

1.1 Compounds Studied

一一Boro・Carbides& Chevrel-Phase Compounds

Since the beginning of出iscentury when H. Kamelingh Onnes discovered supercon-

ductivity in mercury [1.1]， search for new superconductors with higher transition tem-peraもures(Tc) has its own long history unti1 today. In Fig. 1.1， the most simplified

history of the highest Tc is shown with some other interesting compounds [1.2]. Search-

ing for superconductivity in elements ended by 1930's， followed by the trial on binary

compounds. This leads to the discovery of the A15 compounds， which are now com-

mercially used. In fact， Nb3Ge had retained the highest Tc (23 K) until the cuprate

superconductors appeared in 1986.

Seeking for ternary superconductors also continued at the same time， which brought

about the discovery of the Chevrel-phase compounds as one of the most prominent re-

su1ts of this trial [1.4]. In 1971， Chevrel et al. [1司reportedthe presence of a new family

of ternary molybdenum sulfides， which are written as the general formula AxMo6XS (X

= S， Se， or Te and A can be a町 metalelement). 111 1972 Mattias et al. [1.5] reported the

superconductivity of many compoullds of this family. This Chevrel-phase compounds

have interested mally researchers Ilot ollly ill that their cluster structures are quite diι

fernect from structures of billaries but also in that unusual are mally physical properties

of this group of compounds， for example， quite a high critical maglletic field HC2 in

PbMo6SS and competition between superconductivity alld magnetism as observed in

HoMoぬ [1刈.

1

2 CHAPTER 1. INTRODUCTION

60

History of Critical Temperature

Cuprate

40

g 30~ J ~3Cω

トO Nb3Sn Nb3Ge |BKBO

• ‘ U....~I V内 SI. 冨

〈!帆c・10ト Pb Nb-1 U;i204 ~bM06S8

O 1920 1940 1960 1980

Year

Figure 1.1: History of the increase of the highest superconducting transition tempera-

ture (Tc).

Even after the discovery ofthe cuprate superconductors， search for superconductors

except cuprates also has continued. In this process， newly discovered are some other

'exotic' s叩 ercondutorssuch as Bal-xKxBi03 (BKBO) and K3C60 [1.7). They have

rather high Tc's which might result from their own characteristic structures. To add

to their appearence， a new large group of superconducting materials were discovered

in 1993 by Nagarajan et αl. [1.8) and Cava et αl. [1.9). They are nickel boro-carbides

with the general formula L州 i2B2C(Ln = Y， Lu， Er， and so on. Ni can be replaced

by Pd or Pt). They show rather high Tc (Tc = 16.6 K for LuNi2B2C and 23 K for

Y-Pd・B・C)in spite of the inclusion of late transition metals such as Ni. In addition，

competition between superconductivity and magnetism is observed in HoNi2B2C [1.10]

as in the Chevrel-phase compounds.

1.2. PHOTOEMISSION SPECTROSCOPY 3

As described above in quite a simple way，もhereseem to be many ways to new

superconductors to be discovered and in fact various compounds seem to exist. It is

di伍cultto classify them， but one of the most well-known universal relationships among

them is the γ-Tc plot， where γstands for the electronic specific coe伍cient.In Fig. 1.2

is shown the plot [1.7， 11]. It is clear from the figure that γand Tc are correlated with

each other strongly. In the BCS theory， T c is given by [1.12]

Tc = 1.44ωDexp(--i-) Vρ(EF) "

(1.1)

where WD stands for the Debye frequency， V for the electron-phonon coupling strength，

and ρ(EF) for the density of states at the Fermi level. On the 0もherhand， the electronic

specific coe血cientis expressed in the free-electron model as

γ=ト2ρ(EF)kB2

(1.2)

where kB is Boltzmann constant. Then， it follows that Tc monotonously increases with

γ， although this view is too much simplified and there are many exceptions such as

heavy-fermion systems in Fig. 1.2.

Judging from Eq. (1.1)， higher ρ(E F) or larger V is favorable for higher T c. In

fact， many superconductors with higher Tc's in Fig. 1.2 include elements with d bands，

which have localized nature and tend to form narrower bands than s-p metals. In this

respect， the borcトcarbidesand the Chevrel・phasecompounds have close relation with

each other as shown in the figure.

In this thesis， we will study the electronic structures of the bo町r仁かト同carbidesand the

Chev円rel-p

r問esωolutionmeasurements in Chapters 2 and 3， respectively. ln addition， comparison

with the band-structure calculations will be performed.

1.2 Photoemission Spectroscopy

The technique of photoemission spectroscopy has been widely used as one of the most

suitable methods by which the electronic structure of solids can be revealed. In this

section， we will summarize the principle of this method which has been adopted to

our study [1.13]. Details as to the real experiments will be reported in the following

chapters.

INTRODUCTION CHAPTER 1.

YBCO

|A 15 compounds I

PbM06S8

06S8 • LiTiP4 Nb _

・ 13-La V.・• α-La

• •

MoC Nb3G

Tac-:Nb3Sn NbN

-Ta

Pb • α-Hg NaWO.， • 13-Hg ・3A.

- t>n In

TI •

BKBO • -BPBO

4

(X)。ト Chevrel-phase compounds Re

• -・ThNbO

円u・.Ti

Os.. Zr

AI.

Mo ・

• C8K

• SrTi03

n

マι

a

・.G

-Cd

2

auaU

4EE

2

4

1000 10 100

'Y (mJ / (mol.K2))

0.1

Figure 1.2: Plot of Tc against the electronic specific heat coe伍cientγ.


An electron which absorbs a phoもonwi th energy hωcan be emitted from the solid

as a photoelectron. In this process， the energy conservation rule holds:

Ekin = hω-φ-EB， (1め

where Ekin stands for the energy of the emitted electron，ゆ forthe work function of the

solid under study， and E B for the binding energy. As shown below in Eq. (1.9)， EB

corresponds to the electron energy measured downward from the Fermi level in the one-

electron approximation. Ekin is measured from the vacuum level. In real experiments，

however， the kinetic energy measured from the Fermi level (Ekin) is directly observed

rather than Ekin. The following holds in this notation:

Ekin =払u-EB. (1.4)

Utilizing this "equation， the electronic structure of the occupied states such邸， the core

levels and the valence band， can be obtained by measuring the energy spectrum of

photoelectron as shown in Fig. 1.3. In the same way， the inverse-photoemission spec-

troscopy reveals the electronic structure of the unoccupied states by sending electrons

of varying energy onto a sample and detecting the photons produced by them.

Photoemission process results from the excitation of electrons from the initial state

i with its energy Ei to the final state f with its energy Ef by the photon field. In the

dipole approximation， the transition probability ωof this process can be calculated by

Fermi '8 Golden Rule or the first-order Born approximation as follows，

ωα与I(刀rli)128(Ef一Ei一恥) (1.5)

Then， the photoemission"spectrum I(EB)ωa function of the binding energy (E B) can

be expressed using Eq. (1.4)

I(EB)ぼ乞IUlrli)128(Ef-Ei -nw). (1.6) f

To discuss the transition matrix element Ulrli)， it is assumed that the initial-state

wave function with N electrons is written as a product of that of the orbital Oki from

which the electron is excited and the wave function of the remaining electrons (宙f-1).

o refers to the initial ground state， and superscript N -1 to the number of remaining

electrons. In this approximation， the following holds

li) = Iゆk;)I世f-l).


b Spectrum Obtained

hv

d

d

印CJU e

仰E

QU

弘一中一

h

CoreLevels

Nの

Figure 1.3: Schematic diagram of photoemission spectroscopy.

In the same way， the final state is expressed as a product of the wave function of the

photoemit刷伽tronゆJkinwith the energy Ekin and that of the remaining electrons

可-1with N -1 electrons出 follows:

11) = I<TJ川Then the dipole-transition matrix element in Eq. (1.5) may be rewritten as

Ulrli) = (<TJkin Irl九)(宙7-11吋-1) (1. 7)

In the so-called frozen-orbitalα，pproX'trrLαtion the orbital relaxation is neglected， which

means that the initial a凶 thefinal states of the remaining (N -1 )-electron systems

can be regarded as the same and therefore世71=吋-1holds. Then the fol1owing

can be proved:

Ekin =払d十 fki. (1.8)


Here， Ek; is the Hartree-Fock orbital energy of the orbital ki called Koopmαns' binding

energy. Then the meaning of the binding energy E B is clear now

EB = -Ek;' (1.9)

To add to this approximation， if we assume that the dipole-transition matrix element is

constant， which is true at least in x-ray photoemission spectroscopy， Eq. (1.6) becomes

I(EB)αL8(EB +句 )αρ(-EB)， (1.10)

which gives the density of states of Bloch electrons (ρ) in the solid under study. (In the

angle integrated mode， it is necessary to sum over kd When the orbital relaxation cannot be neglected， Eq. (1.6) must be calculated by

summing allpossible excited states. If E~-1 is the energy of the excited state n of the

(Nー1)-electronsystem with the wave function世ご-1，then Ef is equal to E~-I+Ekin ・

Therefore， EB gives the difference between E: and E;:-I. It yields:

I(EB)α乞1(仲間Irlゆk;)12L ICn，ki 1

28(EB 一 (E:-E;:-I))， (1.11)

with

Cn，k; = (申~-11宙~-1) = (世ご-11αk;1宙~). (1.12)

αk; is the annihilation operator of the electron occupying the orbital ki. len，ki 12 is the

probability that the removal of an electron from orbital ki of the N-electron ground

state leaves the system in the excited state n of the (Nー 1)モlectronsystem.

In terms of Green's function formalism， Eq. (1.11) can be rewritten in another

expression [1.14]. Let the Green's function G(k， t) defined邸 follows:

G(k， t) 三 -i(世~IT[ak(t)al(O)lI 曽~)， (1.13)

where αk (al) is the annihilation (creation) operator of an electron with momentum

k and T is Wick's time-ordering operator. By Fourier-transforming Eq. (1.13)， the

well-known formula called Lehmαnn representation can be derived:

f∞ Ak(z) ， fμA~(z) G(k，ω) = 1 dz . --It.'-，' ~__ + 1

Jμω -z十 Zη J-∞ ω -z-zη

where μstands for chemical potenもialand

Ak(z) =乞I(可+llall吋)128(zー (Ef+1一時))

(1.14)


and

AZ(z) =乞I(ザ-11αkl吋)12o(z一 (E:-E~-I)).

Ak(z) and A~(z) are calledelectron and hole spectral functions， respectively. Using the

identity

1 _ 1 一一一 =p一平付o(x)，Z土切

it is deduced for the hole part of the Green's function

め )=jImGM

Finally， we obtain the Green's function formalism for Eq. (1.11) as follows:

明)守I(計 Irlゅん)|2;ImGMB)

(1.15)

(1.16)

(1.17)

If it is assumed again that the dipole-transition matrix element is constant， the formula

usually used in photoemission spectroscopy is finally obtained:

防 (1.18)

Now it becomes clear that the imaginary part of the Green's function can be measured

by photoemission spectroscopy. In the same way， the electron spectral function A~ is

measured by inverse-photoemission spectroscopy.

References

[1.1] H. Kamelingh Onnes， Akad. van Wetenschappen (Amsterdam) 14， 113818 (1991)

in C. Kittel， Introduction to Solid Stαte Physics， 2nd ed.， (John Wiley & Sons，

New York， 1959).

[1.2] J. C. Phillips， Physics 01 high-Tc superconductors， (Academic Press， London，

1989).

[1司R.Chevrel， M. Serge瓜 andH. Prige肌 J.So1. State Chem. 3， 515 (1971).

[1.4]の.Fischer， Appl. Phys. 16， 1 (1978).

[1.5] B. T. Matthias， M. Marezio， E. Corenzwit， A. S. Cooper， and H. E. Barz， Science

175， 1465 (1972).

[1.6] Superconductivity in Ternary Gompounds Vols. 1 and 11， edited byの.Fischer and

M. B. Maple， (Sprir伊 r・Verlag，Berlin， 1982).

[1.可 T.Tsunetou， Superconductivity and Superfluidity (IwaI則 ni，1993)， p. 158， in

Japanese.

[1.8] R. Nagarajan， C. Mazumdar， Z. Hossain， S. K. Dhar， K. V. Gopalakrishnan， L.

C. Gupta， C. Godart， B. D. Padalia， and R. Vijayaraghavan， Phys. Rev. Lett.

72， 274 (1994).

[1.9] R. J. Cava， H. Takagi， B. Batlogg， H. W. Zandergen， J. J. Krajewski， W. F.

Peck， Jr.， R. B. van Dover， R. J. Felder， T. Siegrist， K. Mizuhashi， J. O. Lee， H.

Eisaki， S. A. Carter， and S. Uchida， Nature 367， 146 (1994).

[1.10] H. Eisaki， H. Takagi， R. J. Cava， B. Batlogg， J. J. Krajewski， W. F. Peck， Jr.，

K. Mizuhashi， J. O. Lee， and S. Uchida， Phys. Rev. B 50， 647 (1994).

9

10 REFERENCES

[1.11] H. Takagi， R. J. Cava， H. Eisaki， J. O. Lee， K. Mizuhashi， B. Batlogg， S. Uchida，

J. J. Krajewski， and W. F. Peck， Jr.， Physica C 228， 389 (1994).

[1.12] C. Kittel， Introduction to Solid Stαte PIゅ ics，2nd ed.， (John Wiley & Sons， New

York， 1959).

[1.13] S. Hufner， Photoelectron Spectroscopy (Spri時 er-Verlag，Berlin， 1994); G. K.

Wertheim and P. H. Citrin， in Photoemission in Solids， edited by M. Cardona

and L. Ley (Springe

[1.14] e.g. A. L. Fetter and J. D. Walecka， Quantum Theory 0/ Many Pα巾 clePhysics

(McGraw-Hill， New York， 1971).

Chapter 2

Photoemission Study of

Ni Boro・Carbides

2.1 Overview

2.1.1 Physical Properties of BOI・o・carbides

Cl'ystal Structures of Boro・carbides

The newly discovered boro・carbidesLnT2B2C [2.1-3] belong to a new group of type 11

superconductors (Ln = Y， Lu， Ho， Tm， Er etc. and T = Ni， Pd or Pt). They have

the same crystal structures as shown in Fig. 2.1 [2.4]. The structures can be regarded

as a type of tetragonal body-centered ThCr2Si2， but a carbon atom is inserted in the

Ln layer. As a resu1t， the boro-carbides seem to consist of a1ternating LnC and Ni2B2

layers implying two dimensionality， whereas the transport measurements show only

weak anisotropy and the band-structure calculations have shown the borか carbidesto

have 3D raもherthan 2D character. The change of the teもragonallattice parameters in

goingfrom Ln = Lu to La， i.e. with increasing lanthanide ionic radius， are also shown

in Fig. 2.2 [2.4]. As the radius increases， the NiB4 tetrahedral angle increases， which

results in the significant decrease in the c parameter.

Superconductivity

The borかcarbideshave rather high critical temperatures (Tc = 16.6 K for LuNi2B2C

and = 15.6 K for YNi2B2C) although the late transition metal element Ni is contained.

11

12 CHAPTER 2. BORO-CARBIDES

LuC

Ni2B2

LuC

Ni2B2

LuC

Ni2B2

LuC

Ni2B2

LuC

Figure 2.1: Crystal structure of LnNi2B2C.

As discussed in Sec. 1.1 (see Fig. 1.2)， these intern凶 alliccompounds fall into the same

region in the 'Y-Tc plot [2.5J (γelectronic specific heat coe血cient)as the A15-type

compounds and the Chevrel-phase compounds， where both γand Tc are relatively high.

Indeed， competition between superconductivity and magnetism [2.6J in HoNi2B2C， for

example， is reminiscent of that in HoMo6S8， one of the re司 entrantsuperconductors

[2.7]. Also， the Tc and the estimated thermodynamic critical field Hc of L州 i2B2Care

comparable to those of A15勾 pecompounds [2.5J.

Band-Structure Calculations

Band-str凹 turecalculations using the local-density approximation (LDA) for L州 i2B2C

(Ln = Y， Lu and La) have been reported by Mattheiss et al. [2.8， 9]. The results of

superconducting YNi2B2C and non-superconducting LaNi2B2C are shown in Fig. 2.3.

According to them， superconducting YNi2B2C and LuNi2B2C have a high density of

states (DOS) at the Fermi level (EF) as shown in Fig. 2.4 for the Y compound， which

is also the case in the cuprates [2.10]， A15・typecompounds [2.11]， Chevrel-phase com-

pounds [2.7J and doped fullerenes [2.12]， although these compounds have quite different

crystal and electronic structures. In the borか carbides，although the Ni 3d orbital com-

ponent has a dominant contribution at EF， the atomic orbitals of all the other elements

13 OVERVIEW 2.1.

Ce3+ • -Ce4+

10.8

-Ce3+

a

u

d品TnJ』

nu

マ'

n

u

n

u

n

u

n

u

q

u

(〈)吉何日ωC0000一口伺」

-6C00伺』窃↑

3.8

3.5

3.6

1.10 0.90 0.95 1.00 1.05 Lanthanide Radius (A)

0.85

Figure 2.2: Tetragonal lattice constants α(bottom) and' c (top) of LnNi2B2C as a

function of the lanthanide radius.

also have significant partial D08 at E F 部 pointedout in Ref. [2.13]， which is dearly

seen in Fig. 2ιThe high Ni 3d partial density of states (D08) at EF suggests that

electron correlation may be significant. In fact， a 11 B NMR study [2.14] indicates that

組 tiferromagneticspin fluctuations appear in the normal state of LuNi2B2C， and fur-

ther， the electrical resistivity is proportional to T2 at low temperatures [2.15] as shown

in Fig. 2.5.

Motivation

Photoemission spectroscopy is one of the most suitable methods for investigating elec-

tronic states in solids. For YNi2B2C， we have observed [2.16] a twかholebound-state

satellite of Ni 3d origin at a binding energy (EB) of "，8 eV using the resonance photoe-

2.1.2

BORO-CARBIDES

n

U

A

U

F-(zootcコE〉

@)ωOH何XW』

ob一ωcoo

CHAPTER 2.

FN

・

ρBaB-

nJ』-EE一

M

N

Y

g

EL

Total

10

2

14

.~巴‘・Yor La

Ni2

2

，'" ..

-_. 82

。

Ru

nJ』

nU4E

・-5

'‘ . 10 5 0

Binding Energy (eV)

Figure 2.3: Band-structure DOS for YNi2B2C (the solid line) and LaNi2B2C (the dashed

line) [2.8， 9].

15

cnN・

鳥島，一のF

』・'E

一

M

N

Y

U

OVERVIEW

• • • •

~-• • • • • • • • • • • • • • • • • •

Total

2.1.

82

れ「

nunu

n-』

4E

nunU

F

・(=φozcコz〉

O)ωφ戸何日

ω』

ohv一ωcoo

O

0.4

0.2

0.0

1.0

0.0

2.0

0.00

0.10

-1.0 0.5 0.0 -0.5 8inding Energy (eV)

1.0 0.00

Figure 2.4: Band-structure DOS for YNi2B2C (the solid line) and LaNi2B2C (the dashed

line) near EF [2.8， 9].


40ト 6卜

)

E b

I / YNi2B2C

I/lNi2B2 plane LL/. o 100 200 300

Temperature (閃

Figure 2.5: Temperature dependent resistivity for single crystal YNi2B2C with the

current parallel Ni2B2 plane [2.15]. The inset shows thatもheresistivity is proportional

to T2 in the normal state.

mission technique. The results suggest that electron correlation is significant in the Ni

3d band and the on-site d-d Coulomb interaction energy is as largeω ，，-，5 eV. We have

also observedもhata DOS peak at EF which is predicted by the band-structure calcu-

lations is suppressed and the lost spectral weight is transferred away form EF. Golden

et al. [2.1司havealso reported the same Ni satellite in the photoemission spectra. Pel-

legrin et α1. [2.18] have measured Ni 2p and B 1s core level X-ray absorption (XAS)

spectra and found a similarity between the-two XAS spectra， which they attributed to

strong Ni 3d-B 2p hybridization asshown in Fig. 2.6.

In what follows [2.16]， we report on a compa凶 ivestudy of the electronic structures

of the superconductor YNi2B2C and the non-superconductor LaNi2B2C. We have chosen

YNi2B2C rather than a Lu compound， because Y has no 4f electrons and therefore

the valence band spectra will not be obscured by the 41 multiplet splittings. Here we would like to emphasize that it is not trivial why LaNi2B2C shows no superconductivity

because La is no∞n-別"弓I訂ma

change in the coordination geometry of the NiB4 tetrahedra induced by the change of

Ln from YもωoLa has a great in自uenceon the s-p band of B n町ea町rE F. J udging from

Fig. 2.2， it is clear that the La compound has quite a different geometry than the other

2.1. OVERVIEW 17

K

L

一一(g一ロロ

.fω)ロ。一五』

02〈 c

185 190 195. 200 Photon energy (e V)

Figure 2.6: Comparison of theNi 2P3/2 and B 1s x-ray absorption edges of

ErNi2B2C [2.18].

borcトcarbides.As a resu1t， LaNi2B2C has a smaller DOS at EF than YNi2B2C. The

results of the band-structure calculations are shown in Figs. 2.3組 d2.4. This sizeable

effectaccompanied by the coupling between the electronic state at EF 組 dthe boron A1g

phonons is proposed to be essential in the appearance of superconductivity [2.9]. In this

respect， comparative photoemission and inverse.，photoemission spectroscopy studies of

both compounds are of great interest.

First1y， we shall report the core-Ievel spectra， which tells us their bonding characters (in Sec. 2.3.1). In addition， we have observed satellites derived from twcトholebound

states in出eNi core-level spectra suggesting that electron correlation is significant in

both compounds. In Sec. 2.3.3， we show the spectra for YNi2B2C obtained by means

of the resonant photoemission technique， which supports our picture of two-hole bound

states [2.16].


Secondly， we shall report the spectra of occupied and unoccupied states around

EF and make a quantitative comparison of them with the band-structure calculations

in Sec. 2.3.5. One would expect different spectra near EF for the two compounds，

accordingもothe above suggestion. However， we have observed that there is little， if

any， difference in the spectra of the occupied states near EF • Moreover the predicted

DOS peak at EF was not observed in the spectra of YNi2B2C. This may indic叫ethat

もheelectronic struc七ureis significantly modified byもheeffects which are not included

in the band-structure calculations such as electron-electron correlation and/or electron-

phonon interaction.

2.2 Experiment

2.2.1 Sample Preparation

Polycrystalline samples of YNi2B2C and LaNi2B2C were prepared by arc-me1ting and

annealing [2.2]. The starting materials were lanthanide metal shavings or sublimed

dendrites (99.9 % or 99.99 % pure)， Ni powder (99.99 %) and coarse C (99.99 %) and B

(99.6 %) powders. Samples of 0.75 g total weight were pressed into 0.25・inch-diameter

pellets， which were then arc-melted under argon atmosphere on a standard water-

cooled copper hearth three times， with the melted butもonturned over between melts.

Annealing the arc-me1ted buttons (wrapped in tantalum foil， and sealed in evacuated

quartz tubes) for 12-36 hours at 1，050-1，100 oC yielded polycrystalline material with

less than 2 % impurity phase presented (Ref. [2.2]).

2.2.2 Photoemission Measurement

X-ray photoemission spectroscopy (XPS) measurements were performed using the Mg

kαline (hll 1253.6 eV) and photoelectrons were collected using a double-pass

cylindrical-mirror analyi:er. Ultraviolet photoemission spectroscopy (UPS) measure-

ments using the He 1 and He II resona恥 elines (hll =21.2 eV and 40.8 eV， respectively)

were made using a hemi-spherical analyi:er. We also measured inverse-photoemission or

Bremsstrahlung-isochromat spectroscopy (BIS) spectra by detecting photons of hll =

1486.6 eV using a quarti: monochromator. Calibration and estimation of the instru-

mental resolution were done using Au evaporated on the surface of the samples after

each measurement. These were performed for XPS by defining Au 417/2 = 84.0 eV， and

2.3. RESULTS AND DISCUSSIONS 19

for BIS and UPS by measuring the Fermi edge. The total resolution was "，1 eV， "'35

meV， "，80 meV and "'0.7 eV for XPS， He 1 UPS， He 11 UPS， and BIS， respectively. XPS

and BIS measurements were made at liquid-nitrogen temperature and UPS measure-

ments at "，25K. We also measured the temperature dependence of the He 1 spectra for

YNi2B2C between 25 K and 200 K. The samples were scraped in situ with a diamond

file and measured under a pressure of 1-4 xl0-10 Torr. Scraping was repeated until the

o Is XPS signal， which indicates surface contamination， disappeared. As the surface

stayed clean for 1-2 hours after scraping， all the measurements were undertaken for

surfaces scraped repeatedly during this interval.

To add to these， for YNi2B2C， we also performed photoemission spectroscopy by

means of synchrotron radiation (SR) including resonance-photoemission spectroscopy

at beamline BL-2 of the Synchrotron Radiation Laboratory， Institute -for Solid State

Physics， University of Tokyo. The total instrumental resolution varied from "，0.3 eV

at hv "，40 eV to "'0.6 eV at hv "，100 eV， which was determined by the width of the

Au Fermi edge. The calibrations were done using the evaporated Au. Measurements

were done at liquid nitrogen temperature with the surface of the sample scraped in situ

with a diamond file.

The measurement conditions reporもedabove are listed in Table 2.1.

2.3 Results and Discussions

2.3.1 Core Levels

YNi2B2C and LaNi2B2C both have Ni， B， and C in common. Therefore it is meaningful

to compare the B Is， C Is and Ni 2p core-level spectra for the two compounds.

The B Is peak position was 188.1 eV and 188.0 eV for YNhB2C and LaNi2B2C，

respectively， as shown in Fig. 2.7. These values are similar to those (186-188 eV)

reported on binary transition-metal borides suchωFeB and CoB by Mav~l et αl. [2.19，

20]. This indicates that in LnNhB2C the character of bonding between Ni and B is

similar to the metal-boron bonding in the simple boride.

Figure 2.8 shows the C Is core-level spectra of both compounds. The structures

around 285-286 eV may be due to surface contamination， because the intensity of these

structures is dependent on samples and， moreover， change after scraping. Therefore，

we have assigned the structures around 282-283 eV to the true C Is signals of the


Table 2.1: Conditions of the measuremen臼 forthe borかcarbides. LNT stands for

liquid-nitrogen temperature. SR means synchrotron radiation.

Conditions for YNi2B2C.

Measurement Photon Energy (e V) Resolution (FWHM) Temperature

He 1 UPS 21.2 rv35 meV 25-200 K

He II UPS 40.8 rv80 meV "，25 K

SR 40， 63， 68， 100 0.3-0.6 eV LNT

XPS 1253.6 "'leV LNT

BIS 1486.6 "，1 eV LNT

Conditions for LaNi2B2C.

1 Measurement 11 Photon Energy (e V) 1 Resolution (FWHM) 1 Temperature J

He 1 UPS 21.2 rv35 meV ，，-，25 K

He II UPS 40.8 rv80 meV "，25 K

XPS 1253.6 "，1 eV LNT

BIS 1486.6 "，0.7 eV LNT

borcトcarbides.

According to Fig. 2.8， the same as above described for B 18 core-levels holds for

the C 18 peak position， which was 282.7 eV and 282.5 eV for YNi2B2C and LaNi2B2C，

respectively. These values are in the same range as the C 18 peak positions (282 eV)

in MC (M = Ti， Zr and Hf) [2.20， 21]， considering that it can vary between 280 eV

and 293 eV from compound to compound [2.20]. The similarity suggests that electrons

are transferred from metal (Ln) to carbon atoms in the nickel borか carbidesas in the

binary metal carbides.

Figure 2.9 shows the Ni 2p core-level spectra of both boro-carbides. To add to this

in Fig. 2.10， the spectra around the Ni 2Pl/2 peak are also shown because in LaNi2B2C

the Ni 2P3/2 and La 3d3/'2 peaks are at the same position. Therefore， the spectra of

both compounds in Fig. 2.9 have been normalb:ed at the Ni 2Pl/2 peak， for which the

positions are 870.7 eV and 870.5 eV for YNi2B'2C and LaNi'2B2C， respectively， while in

Ni metal the peak is at 869.7 eV (Ref. [2.20]). As Pellegrin et al. have remarked [2.18]，

these chemical shifts are supposed to result from charge transfer from the metal atoms


(ωzcコ.0』何

)

LaNi2B2C

YNi2B2C XPS

B1s

、AH

一ωcgc

190 189 188 187 186

Binding Energy (eV)

Figure 2.7: B Is core-level photoemission spectra of YNi2B2C and LaNi2B2C. The peak

positions are marked by vertical bars. The solid lines show smoothed data.

(Ni and Ln) to its non-metal B and C neighbors， which is again consistent with the

above suggestion based on the comparison with the binary metal borides and carbides.

The shape of the La 3d5/2 peak in LaNi2B2C is similar to that in La metal rather th組

ionic compounds like La203 (Ref. [2.22]). That is， the well-screened feature at "，833

eV is much weaker than the poorly-screened peak at "'836.5 eV， reflecting the highly

covalent La-C bonding character.

Thus in going from LaNi2B2C to YNi2B2C， the core levels， of which positions are

listed in Table 2.2， are shifted towards higher binding energy by 0.1-0.2 eV. Since the

crystal structure and the number of conduction electrons are almostもhesame for both，

the core-level shifts may well reflect small differences in bond lengもhsor bond angles

between constituent atoms. In fact， the Ni・Nibond lengths are 2.50 A and 2.68 A (Ref. [2.9]) for YNi2B2C and LaNi2B2C， respectively (see Fig. 2.2 [2.4]). The shorter


o LaNi2B2C ・YNi2B2C

XPS

(ωZCコ.0』何

)

C 1s

、AH

一ωcωHC H

contamination

290 288 286 284 282 Binding Energy (eV)

280

Figure 2.8: C Is core-level photoemission spectra of YNi2B2C and LaNi2B2C. The peak

positions are marked by vertical bars. The solid lines show smoothed data.

bond length tends to increase the width of the Ni 3d valence band， which will raise the

Fermi level since the EF is located near the top of the Ni 3d-derived valence band. This

in turn lowers the core level positions relative to EF. This explains the higher binding

energies of the core levels in YNi2B2C than in LaNi2B2C.

A remarkable feature in the Ni 2p spectra is the existence of a satellite in both

compounds， which is around 861 eV for Ni 2P3/2・ Sucha satellite is well known in Ni

metal and Ni intermetallic compounds [2.23， 24] and is assigned to a "two-hole bound

state" in the core-hole final state， resulting from significant electron correlation within

the Ni 3d band. Indeed， resonance photoemission from the valence band of YNi2B2C

has revealed a satellite around the binding energy of 8-9 eV [2.16， 17] as reported below.

It will be shown that the satellite position is ，，-，7 eV away from the main peak for the

Ni 2P3/2 core level and ，，-，7 eV from the main Ni 3d peak for the valence band (see

Fig. 2.18).

2.3. RESULTS AND DISCUSSIONS

(ωzcコ.2」何)会

ωcsc-

23


XPS hv = 1253.6 eV

La3d

3d3l2 3dS/2

satellite

川 a ↓

a・・a・

890 880 870 860 850 840 830 Binding Energy (eV)

Figure 2.9: Ni 2p core-level photoemission spectra of YNi282C and LaNi2B2C. They are

normalized at the Ni 2Pl/2 peak. The arrows indicate the satellites due to the two-hole

bound state.

Table 2.2: Core-level peak positiolls (eV) of YNi282C and LaNi282C.

Core-level YNi282C LaNi282C

8 1s 188.1 188.0

C 1s 282.7 282.5

Ni 2Pl/2 870.7 870.5

BORO-CARBIDES CHAPTER 2. 24

XPS

城

、-F h

ヘ."、.

、a

・

}--・・ι司

、.、.4

・'}4・eJS

F "、

・司

“

一一一切

Ni 2P1/2

0

0

0

。。

。句。。。。。

cc

民B

一

nJ』

'a一

N

N

aY

『

LO

• (ωtcコ.2』何)会

ωCOVE-

866 868 872 870 Binding Energy (eV)

874 876

Figure 2.10: Ni 2Pl/2 core-level photoemission spectra of YNi2B2C and LaNi2B2C. The

peak positions are marked by vertical bars.

Finally， the Y 3d core-level spectra of YNbB2C and the La 4d core-level spectra of

LaNi2B2C are shown in Figs. 2.11 and 2.12.

Valence-Band Photoemission Spectra

Figure 2.13 shows the valence-band XPS spectra of YNi2B2C and LaNi2B2C measured

at liquid-nitrogen temperature and the He 1 and He II UPS spectra measured at "，25 K.

These spectra have been normalized to the peak height. To what extent the contribution

2.3.2

of each constituent element appears in the spectra depends 011 the cross-sections as

shown in Fig. 2.14 (Ref. [2.26]).

The XPS spectra of both compounds are ShOW11 at the top of Fig. 2.13. The satellite

structure due to the twか holebound state at binding energy EB "，8 eV is weak. (The


.2」何)

喜引|い|γY判川Ni2仇2コ

Y3d

XPS hv = 1253.6 eV

、222c

180 170 160 Binding Energy (eV)

150

Figure 2.11: Y 3d core-level photoemission spectrum of YNi2B2C. The solid line shows

smoothed data .

• 0』

伺

)

さ11LaNi2B2CIコー

XPS hv = 1253.6 eV

hv

一ωcoHF』

130 125 120 115 11 0 1 05 1 00 95 Binding Energy (eV)

Figure 2.12: La 4d core-level photoemission spectrum of LaNhB2C. The Ni 38 core

level is located close to the La 4d core level.

26

•

CHAPTER 2.

LaNi2B2C

YNi2B2CI hv = XPS 1253.6 eV

Hel hv = 21.2 eV


BORO-CARBIDES

O

Figure 2.13: Valence-band photoemission spectra of YNi2B2C and LaNi2B2C.

2.3. RESULTS AND DISCUSSIONS

10 もσ3

Z 0 4・4

0 〉

何

Q)

庄

C 0

~ 0.1 cn ω ω 。‘-O 2

2 4 6 8 100

2 4

ベ子 Y-0-La

→← B -← C 『・-Ni 6

27

Photon Energy (eV)

Figure 2.14: Cross-sections per electron of the atomic orbitals relative to Ni 3d [2.26].

satellite in the XPS spectra can be identified as an excess intensity at EB rv8 eV

compared to the band structure calculation， see Fig. 2.20 and Sec. 2.3.5) Judging from

Fig. 2.14， the XPS spectra reflect mainly Ni 3d character. The He-II UPS spectra

are shown in the middle panel of Fig. 2.13. Considering the photoionization cross-

sections， the He II spectra reflect more B and C 2sp character than the XPS spectra.

The intensity of the He II spectra at EB > 4 e V is stronger than that of the XPS

spectra， which indicates the existence of a broad B and C 2sp band at EB > 4 eV.

The He 1 spectra are also shown at the bottom of the Fig. 2.13. Much more B and C

2sp and much less Ni 3d character should appear in the He 1 spectra than in the He II

spectra according to Fig. 2.14， and therefore the feature around 4-5 eV is certainly of

B and C 2sp character. These results agree well with those of B Is soft X-ray emission


spectroscopy (SXES) [2.25]， which show a large peak around 4-5 eV for both compounds

as shown in Fig. 2.15. However， there are additional intense features around 6-7 eV

in our He 1 spectra. They may be due七osurface contamination in grain boundaries of

the polycrystalline samples， because the bulk-sensitive SXES spectra shows no such a

feature there.

(ω芯ロロ-A』MW)

円凶¥k内判明ωロωEH

YNi2B2C . 20 K (a)

K

AU

勺'uc

q

，-B

今'b

N

9u

T-U (的判明ロコ・D』同)門凶

¥hZ凶ロ旦ロH

15 。

Figure 2.15: B 1s SXES spectrum of YNi2B2C and LaNi2B2C. The dashed lines are the

calculated B 2sp partial DOS and the solid lines are the broadened DOS (Details are

given in Fig. 2 of Ref. [2.25].)


In the He 1 spectra of the two compounds， the main peak due to Ni 3d is at the

same position and the intensity just below EF is essentially the same， which is also the

case for the He 11 spectra. The intensity just at EF relative to the intensity of the peak

at rv1.4 eV increases in going from hll = 21.2 eV to hll = 40.8 eV. Because the relative cross-sections of Ni 3d to B and C 2sp increases when going from hll = 21.2 eV to

hll = 40.8 eV部 shownin Fig. 2.14， we may say that the contribution of Ni 3d is large

at EF in both compounds. The spectra of YNi2B2C and LaNi2B2C closely resemble

each other at each photon energy， while they differ in that the YNi2B2C spectra show

a shoulder structure around 2 e V [2.25] but that no such structure can be seen in

the LaNi2B2C spectra. The presence of the shoulder structure is consistent with the

band-structure calculations as discussed below.

In addition， we have measured spectra of YNi2B2C near EF in detail with changing

temperature from 25 K to 200 K as shown in Fig. 2.16. As the temperature increases，

the slope of the spectrum at the Fermi level decreases systematically， which can be

explained by the temperature dependence of the Fermi-Dirac distribution function. We

find no evidence for the peak at EF predicted by the band-structure calculations.

(ωtcコ

1ヤ一一崎→両一曲-〈抑制

|YNi2B2C|

時『、、自:'"""皿、ド¥、200K

~円九~¥¥¥100 K 、~咋可酬明 W'OIII ・~喝、 h .. 50 K

Hel ¥~… F '

hv = 21.2 eV 25 K

.2』伺

)

』

AH

一ωcgc

0.3 0.2 0.1 0.0 ・0.1

Binding Energy (eV)

Figure 2.16: Temperature dependence of the UPS spectra of YNi2B2C near EF.


2.3.3 Resonance-Photoemission Spectra of YNi2B2C

For YNi2B2C， we performed resonance-photoemission spectroscopy by means of syn-

chrotron radiation. The principle of resonance-photoemission is as follows. When we

make the incident photon energy match the energy of the absorption from the core level

(Ni 3p in山iscase) to the valence band (Ni 3d)， resonance-photoemission occurs. In

this process， the following two processes interfere quantum-mechanically to result in

the enhancement of the cross-section of the corresponding valence band [2.27]:

• Usual photoemission process:

Ni 3d8 + hv→ Ni 3d7 + e-.

• Ni 3p core level absorption followed by a kind of Auger process called super

Koster-Kronig transition:

Ni 3p63d8 + hv→Ni 3p53d?→Ni 3p63d7 + e-.

To take the advantage of the fact that the photoionization cross-section of the Ni 3d

orbitals greatly changes below and above the absorption threshold， we can distinguish

the Ni 3d component in the valence band spectra.

The result is shown in Fig. 2.17. On-and off-resonance occur at the photon energies

hν= 68 eV and 63 eV， respectively. There is also shown the difference spectrum between

the 68 eV and 63 eV spectra at the bottom of the figure. It is clear that the intensity

around ""'8 eV increases at on-resonance， which indicates that the ""'8 eV satelliもeoccurs

due to a twか holebound state through significant electron correlation within the Ni 3d

band. It is not the main line EB "̂' 1.5 eV but the satellite whose intensity is enhanced

mainly at on-resonance as described in Ref. [2.27]. These results [2.16] are consistent

wi th the report by Golden et αl. [2.17].

Qne can also compare the result of the resonant-photoemission spectra and that of

the Ni 2p core level spectra as shown in Fig. 2.18. It becomes apparent that the satellite

position is ""'7 eV away from the main peak for the Ni 2P3/2 core level and ""'7 eV from

the main Ni 3d peak for the valence band， which support the above discussion. It is

emphasized here that the satellite can also be seen at almost the same position in the

Ni 2P3/2 core level spectrum of LaNi2B2C， which indicates that the electron correlation

is significant in this compound as well as in YNi2B2C.

31

• • • •

RESULTS AND DISCUSSIONS

，

，

-一一-/，d'守- - - - 一 '

|YNi2B2CI

hv = 100 eV

一一一一

hv = 68 eV

hv = 63 eV

2.3.

(ωtcコ.esEωcsc-

satellite

〆

O 12 8 4 Binding Energy (eV)

16

Photoemission spectra of YNi2B2C for various photon energies.

is also shown the difference spectrum between the 68 eV (on-resonance) and 63 eV

There Figure 2.17:

(0宜・resonance)spectra at the bottom of the figure.

BORO-CARBIDES CHAPTER2. 32

850 852

O

O

O

O O O O. O O •

854

• • • • • • • • •

856 858

satellite due to two-hole bound state

860

cc

民B

一2自宅

M川

M川

aY

EL

862

O

• 864

(ωtcコ.2』何

)b一ωcsc-

XPS hv = 1253.6 eV

hv = 63 eV

-2 O 8 6 4 2 Binding Energy (eV)

10 12

Figure 2.18: Comparison between the resonant-photoemission spectra and the Ni 2p

core level spectra.


The spectrum obtained at hν= 100 eV is also shown on the top of Fig. 2.17 [2.16].

It is of use to compare the two spectra taken at hν= 63 and 100 e V a.s we have done in

Sec. 2.3.2. As shown in Fig. 2.14， when the incident photon energy is varied from 63 to

100 eV， the relative cross section of B and C 2sp to Ni 3d decrea.ses. Then comparing

the two spectra with the band-structure calculations， it is noticed that the features at

EB "，10 and "，14 eV which are stronger in intensity for hν= 63 eV than for hν= 100

eV indicates that they are of B-and C-hybridized character. Though "，，1 eV shifted to

higher binding energy， these features are consistent with the band structure calculation.

Although there is a small but distinct feature at EB = 6 eV， it may not be intrinsic

but due to surface contarnination a.s is discussed in Sec. 2.3.2. These assignments are

also verified by the B ls SXES a.s shown in Fig. 2.15.

2ふ 4 BIS Spectra

Figure 2.19 shows BIS spectra of YNi2B2C and LaNi2B2C. One can immediately know

from Figs. 2.3釦 d2.14 that the features in the BIS spectrum ofYNi2B2C are mainly due

to the Ni 3d and Y 4d. Then， in accord組 cewith the band-structure calculations， the

feature located from EF to "，1.5 eV above it is assigned to the Ni 3d-derived conduction

bands and the broad one centered at ，，-，5 eV above EF to Y 4d character.

For LaNi2B2C， the intense peak at ，，-，6 eV above EF is shown in the spectrurn，

which is舗 signedto the La 41 empty states while the band-structure calculations [2.9] have predicted the 41 states to be around 3 eV above EF. In order to subtract the

insuence of the La 41 peak from the spectrum， we have performed a line-shape fitting

of this peak under the assumption that the peak is given by a convolution of Lorentzian

and Gaussian functions， corresponding to the lifetime broadening and the instrumental

resolution， respectively. The result is shown in Fig. 2.19 by a da.shed line. The solid

line is the difference between the spectrum and the fitted curve. We thus find that the

La 41 peak ha.s litt1e infiuence on the spectrurn near the Fermi level， and therefore we

can cornpare the BIS spectrum of LaNi2B2C with the band-structure calculations a.s

described below.

BORO-CARBIDES CHAPTER2. 34

八。一818

hv = 1486.6 eV 。

。。。

。。。

。。

。。。。

¥ difference

(ωtcコ.2」何)kAH

一ωcsc-

6 024 Energy relative to EF (eV)

ー2

Figure 2.19: BIS spectra of YNi2B2C and LaNi2B2C. The dashed line is a fitted line-

shape for the La 4f empty states.



We have performed detai!ed comparison between the photoemission spectra and theか

retical spectra derived from the band-structure calculations [2.8，9]. The result is shown

in Figs. 2.20， 2.21 and 2.22. To obtain the theoretical photoemission spectra， the partial

DOS of each atomic orbital component， namely the La 5d or Y 4d， Ni 3d， B 2sp and

C 2sp partial DOS， have been added after having multiplied by the corresponding phか

toionization cross-sections at each photon energy (Fig. 2.14). Then this weighted DOS

has been broadened by convoluting with a Gaussian and a Lorentzian which represent

the instrumental resolution and the lifetime broadening， respectively. We postulate that

the lifetime width is linear in energy E measured from EF， i.e. FWHMω=αIE-EFI， where the constant αis a parameter which is determined so槌 towell simulate the

measured spectra. For both compounds we have taken α= 0.30 for the photoemission

spectra. 1n simulating the spectra， we have also added an integral background due

to secondary electron emission as shown by dashed lines in Figs. 2.20， 2.21 and 2.22.

Normalization between the experimental and theoretical spectra has been done at the

peak height.

To obtain the theoretical B1S spectra， we have proceeded in the same way as for the

photoemission spectra， except that we have taken α= 0.20. The B1S spectra refiect

the Ni 3d and Y 4d or La 5d components of the empty states because theB and C 2sp

components have small cross-sections at hν= 1486.6 eV and small DOS above EF [2.8，

9]. As for the B1S spectrum of LaNi2B2C， however， the calculated DOS cannot be

directly compared with the experimental data because of the large discrepancy in the

position of the La 41 empty state. Therefore we compare the Ni 3d partial DOS plus the La 41 peak which has been fitted to the Lorentzian-Gaussian剖 describedabove

and shifted to "，6 eV above EF (Sec. 2.3.4)ωshown in Fig. 2.20. The normalization

between the photoemission and B1S spectra in Fig. 2.20 has been done so that the

measured spectra nearly match the calculated DOS.

Comparison between the experimental photoemission spectra and the theoretical

ones supports our discussion in Sec. 2.3.2. The feature due to the broad B and C

2sp band around 4-5 eV can be seen in the theoretical spectra at hll = 40.8 eV and

1253.6 eV， which agree quite well with the experimental spectra even in the quantitative

sense，錨 inthe case of the SXES四sult[2.25]. The shoulder at "，，2 eV in the measured

spec


(ωZCコ

XPS BIS

ーーーー--... h ... h .

2」何

)

‘・・ ‘・，ーーー

Z||YNi2B2CI Q)

c

-h 崎、

ー・.

-10 -6 -4 ・2 0 Energy relative to EF (eV)

4 -8 2

Figure 2.20: Comparison of the XPS and BIS spectra (dots) with the theoretical spectra

derived from the band-structure calculations [2.8， 9] (solid curves). The dashed lines

show the integral background.


well reproduce the difference between YNi2B2C and LaNi2B2C.

However， some discrepancies exist between theory and experiment. First of all， the

XPS spectra (Fig. 2.20) show additional intensity at EB "，8 eV compared to the band

DOS， which we attribute to a two-hole bound state satellite in analogy with the Ni

core level spectra. Secondly， Figs. 2.21 and 2.22 shows that the DOS peak just at EF

of YNi2B2C is not observed. As for LaNi2B2C， the DOS peak exists about 0.1 eV

below EF in the theoretical spectrum， but there is no sign of the corresponding peak

structure in the measured spectra. Another weak structure around 0.7 eV below EF

seen in the theoretical curve of YNi2B2C is also suppressed. Thirdly， the Ni 3d peak

position EB "，1.4 eV of YNi2B2C is not in good agreement with the band-structure

calculations. At each photon energy， one can see that the peak structure itself is shifted

by "，0.2 e V toward the Fermi level compared to the band-structure calculation. As for

the counterpart in LaNi2B2C， there is better agreement between experiment and theory.

As a result， the shift of the Ni 3d peak in going from YNi2B2C to LaNi2B2C is opposite

between the theoretical spectra and the experimental ones as shown in Fig. 2.23， where

the spectra of the two compounds are plotted together.

One can see in Fig. 2.21 that the theoretical intensity at the Fermi level for hv = 21.2

e V is twice as large掛 theexperimental intensity in both compounds， while that for

hν= 40.8 e V shown in Fig. 2.22 is of the same level， although no peak structure is

observed at either photon energy. This may imply that B and C 2sp weight at EF are

overestimated in the band-structure calculations， since the relative cross-sections of B

and C 2sp to Ni 3d increase with decreasing photon energy (Fig. 2.14).

The theoretical BIS spectra shown in Fig. 2.20 also discriminate between YNhB2C

and LaNi2B2C. In YNi2B2C， the calculated BIS spectrum has a higher intensity at EF

than in LaNi2B2C， refl.ecting the sharp DOS peak at EF in YNi2B2C， but the measured

spectra of both compounds show ordinary Fermi edges. YNi2B2C has an apparent

structure仕om0.5 eV to 1.2 eV above EF which is assigned to the Ni 3d empty states

although it is shifted toward higher energies compared with the theoretical spectrum.

LaNi2B2C， however， has a featureless spectrum near Ep although the theoretical spec-

trum， in which only the Ni and La 41 empty states are taken into account， forms a peak

around 0.5 e V.

The above dis


(ωtcコ


.2」何)

、222c He I

hv = 21.2 eV

ーーーー・・ーーーーーーーーーーーーーー

2.0 1.5 1.0 0.5 Binding Energy (eV)

0.0

Figure 2.21: Cornparison of the He 1 UPS spectra (dots) with the theoretical spectra




(ωZCコ.0』何)会

ωcsc-

C

G白鳥B

一

ιり』'H4

N

N

ay

-L

0

・

ーーーーーーーーー』-..ー--.. -・.. ー『・.-h

ー.. h 、.、

、

句..¥--....

、¥

He 11 伽=40.8 eV

色司、、、

、、色、、、

旬、、、h

h -

h

h

』『

『

-~

』『

---』司

---帽

--


O

Figure 2.22: Comparison of the He 11 UPS spectra (dots) with the theoretical spectra




ω 4・ac コ

一一 LaNi2B2CYNi2B2C

モ BandCalculation ω 〉、4・d

ω C Q)

c

6

Photoemission He 11 hv = 40.8 eV


O

Figure 2.23: Comparison of the He II UPS spectra between YNi2B2C (solid curve) and

LaNi2B2C (dashed curve). The theoretical spectra derived from the band-structure

calculations [2.8， 9] are shown in the upper panel and the experimental spectra in the

lower panel.


in a rnass enhancernent and spectral weight transfer away frorn EF on the low energy

scale. In YNi2B2C， the electronic specific heat coe血cientγis"" 1.8 times enhanced

to be 18.2 mJjmol K2 (Ref. [2.30]) compared to that given by the band-structure

calculations. Electron-phonon interaction rnay be significant because of the existence

of the high frequency boron A1g phonon， whose frequency has been calculated to be 106 rneV (Ref. [2.13]). We stress here that the suppression of the DOS peak at EF

does not rnean a disappearance of the states at EF， but that the lost spectral weight

is transferred to higher energies. As for the opposite shifts of the Ni 3d peak in going

from the La to the Y compounds between the theoretical spectra and the experirnental

ones in Fig. 2.23， electron correlation probably influences the Ni 3d spectral weight

distribution. This does not preclude the possibility that the difference in the B， C

2sp-derived bands as predicted by the band-structure calculations. [2

for the di宜erentsuperc∞onducting properties. Indeed， the SXES study has revealed

differences in the B 18 spectra between the Y and La compounds [2.25] as predicted by

the b加 d-structurecalculations [2.9].

It is instructive to compare the present resu1ts with the resu1ts for similar interrnetal-

lic s叩 erconductors.Figure 2.24 shows a high-resolution photoernission spectrurn [2.31]

of Nb3Al a member of the A15-type compounds. It shows superconductivity below 18.6

K， and has a large DOS at EF according to the band-structure calculation [2.11]. In

addition， the relation between the electronic specific heat coe血cientand the critical

temperature (γ-Tc plot [2.5]) shows that the A15勾 pecompounds are located close

to the Ni borか carbides.We obtain the theoretical spectrum of Nb3AI from the band-

structure calculation as described above. The peak just at EF in the calculated DOS

has been suppressed and the fine structures near EF have been smeared out. This

trend is very similar to the photoernission spectra of YNi2B2C. In the case of Nb3AI，

they rneasured spectra between 10 K and 20 K and observed a spectral modification

due to the opening of a BCS gap， ensuring that the observed spectra reflects the bulk

properties. The disappearance of the DOS peak at E p was previously suggested by Ho

et al. [2.32] in the context of lifetirne broadening due to strong electron-phonon scatter-

ing. On the other hand， it has to be remarked that the angle-resolved photoerniss


(ωzcコ

. --~，. J~--d d

、

Nb3AI

..ci ~"， ‘ー何、‘-

v

e

EEnJ』

e1

H2

am

hzωCOHC

--Photoemission 一一 BandCalculation

2.0 1.5 1.0 0.5 Binding Energy (eV)

0.0

Figure 2.24: Comparison between the experimental spectra [2.31] and the theoretical

spectra derived from the band-structure calculations[2.11] of a A15勾 pecompound

Nb3Al.

2.4 Conclusion

We have measured photoemission and inverse-photoemission spectra of superconduct-

ing YNi2B2C and non-superconducting LaNi2B2C. The core-Ievel spectra well reflect

their bonding character. We have observed satellites due to two-hole bound states in

the Ni core-level and valence-band spectra. The valence-band spectra of both com-

pounds resemble each other and gross spectral features are in good agreement with

the band-structure calculations. The contribution of Ni 3d to Ep is found to be large.

However， there is no sharp DOS peak at Ep， which is predicted by the band-structure

calculations. The discrepancy between the band-structure calculations and experiment

near the Fermi level is larger in YNi2B2C than in LaNi2B2C. The discrepancy between

2.4. CONCLUSION 43

experiment and theory may be due to electron correlation and/or electron phonon in血

teraction which is not included in the LDA band-structure calculations. It is pointed

out that the predicted DOS peak is also absentin other superconductors like A15-type

materials. It remains to be clarified how the observed differences in the spectra of

YNi2B2C and LaNi2B2C and their agreement and disagreement with the LDA band-

structures are related to the occurrence of superconductivity in YNi2B2C.


References

[2.1] R. J. Cava， H. Takagi， B. Batlogg， H. W. Zandergen， J. J. Krajewski， W. F.

Peck， Jr.， R. B. van Dover， R. J. Felder， T. Siegrist， K. Mizuhashi， J. O. Lee， H.

Eisaki， S. A. Carter，組dS. Uchida， Nature 367， 146 (1994).

[2司 R.J. Cava， H. Takagi， H. W. Zandergen， J. J. Krajewski， W. F. Peck， Jr.， T.

Siegrist， B. Batlogg， R. B. van Dover， R. J. Felder， K. Mizuhashi， J. O. Lee， H.

Eisaki， S. A. Carter， and S. Uchida， Nature 367， 252 (1994).

[2司 R.Nagarajan， C. Mazumdar， Z. Hossain， S. K. Dhar， K. V. Gopalakrishnan， L.

C. Gupta， C. Godart， B. D. Padalia， and R. Vijayaraghavan， Phys. Rev. Lett.

72， 274 (1994)

[2.4] T. Siegrist， H. W. Zandbergen， R. J. Cava， J. J. Krajewski， and W. F. Peck， Jr.，

Nature 367， 254 (1994).

[2五]H. Takagi， R. J. Cava， H. Eisaki， J. O. Lee， K. Mizuhashi， B. Batlogg， S. Uchida，

J. J. Krajewski，組dW. F. Peck， Jr.， Physica C 228， 389 (1994).

[2.6] H. Eisaki， H. Takagi， R. J. Cava， B. Batlogg， J. J. Krajewski， W. F. Peck， Jr.，

K. Mizuhashi， J. O. Lee， and S. Uchida， Phys. Rev. B 50，647 (1994).

[2.可S叩 erconductivityin Ternary Compounds Vols. 1 and II， edited byの.Fischer and

M. B. Maple， (Spri昭 er-Verlag，Berlin， 1982).

[2.8] L. F. Mattheiss， Phys. Rev. B 49， 13279 (1994); unpublished results.

[2.9] L. F. Mattheiss， T. Siegrist， and R. J. Cava， Solid State Commun. 91 587 (1994).

[2.10] A. J. Freeman， J. Yu， and C. L. Fu， Phys. Rev. B 36， 7111 (1987).

45

46 REFERENCES

[2.11] B. M. Klein， L. L. Boyer， D. A. Papaconstantopo山 s，and L. F. Mattheiss， Phys.

Rev. B 18，6411 (1978); W. E. Pickett， K.-M. Ho， and M. L. Cohen， Phys. Rev.

B 19， 1734 (1979).

[2.12] S. C. Erwin and W. E. Pickett， Science 254， 842 (1991)

[2.13] W. E. Pickett and D. J. Singh， Phys. Rev. Lett. 72， 3702 (1994).

[2.14] K. Ikushirna， J. Kikuchi， H. Yasωka， R. J. Cava， H. Takagi， J. J. Krajewski， and

W. F. Peck， Jr.， J. Phys. Soc. Jpn. 63， 2878 (1994).

[2.15] H. Takagi， R. J. Cava， H. Eisaki， S. Uchida， J. J. Krajewski， and W. F. Peck，

Jr.， Advances in Superconductivity VII， edited by K. Yarnafuji and T. Morishita

(Springer-Verlag， Tokyo， 1995) p. 9.

[2.16] A. Fujirnori， K. Kobayashi， T. Mizokawa， K. Marniya， A. Sekiyarna， H. Eisaki，

H. Takagi， S. Uchida， R. J. Cava， J. J. Krajewski， and W. F. Peck， Jr.， Phys.

Rev. B 50， 9660 (1994).

[2.17] M. S. Golden， M. Knuper， M. Kielwein， M. Buchgeister， J. Fink， D. Teehan， W.

E. Pikket and D. J. Singh， Europhys. Lett. 28， 369 (1994).

[2.18] E. Pellegrin， G. Meigs， C. T. Chen， R. J. Cava， J. J. Krajewski， and W. F. Peck，

Jr.， Phys. Rev. B 51， 16159 (1995).

[2.19] G. Mavel， J. Escard， P. Costa and J. Castaing， Surf. Sci. 25， 109 (1973).

[2.20] Handbook 01 X-R仰 PhotoelectronSpectroscopy， edited by C. D. Wagner， W. M.

Riggs， L. E. Davis， J. F. Moulder and G. E. Muilenberg (Perkin-Elrner， Min-

nesota， 1978).

[2.21] L. Rarnqvi民K.Harn山， G.Johansson， A. Fal出 lanand C. No凶 ing，J. Phys.

Chem. Solids 30， 1835 (1969).

[2.22] S. Hu出 er，in Hαndbook on the PlゅzcsαndChemistry 01 Rαre Eαrths Vol. 10: High Energy Spectroscopy， edited by K. A. Gschneider， Jr.， L. Eyring and S.

Hufner (North-Holland， Arnsterda瓜 1987)

[2.23] D. R. Penn， Phys. Rev. Lett. 42， 921 (1979); L. C. Davis and L. A. Feldkamp，

J. Appl. Phys. 50， 1994 (1979).

REFERENCES 47

[2.24] S. Hufner and G. K. WertheiI

[2.25] S. Shin， A. Agui， M. Watanabe， M.Fujisawa， Y. Tezuka， T. Ishii， K. Kobayashi，

A.Fujimori and H. Takagi， Phys. Rev. B. 52， 15082 (1995).

[2.26] J.-J. Yeh and I. Lindau， At. Data Nucl. Data Tables 32， 1 (1985).

[2.2可S.Hu血 er，Photoelectron Spectroscopy pp.9仏96(Springer-Verlag， Berlin， 1994).

[2.28] G. A. Sawatzky組 dD. Post， Phys. Rev. B 20 1546 (1979).

[2.29] The La 41 and 5d partial DOS is not given in Refs. [2.8] and [2刈.Although

the cross-sections of La 5d and Ni 3d at hν= 1486.6 eV are comparable， the

calculated partial DOS of Ni is at least twice儲 largeωthatof La in the energy

range between 0-1 eV above Ep， which would justify the comparison between

the measured spectrum and the Ni partial DOS.

[2.30] N. H. Hong， H. Michor， M. Vybornov， T. Holubar， P. Hundegger， W. Perthold，

G. Hilscher， and P. Rogl， Physica C 227 85 (1994); S. A. Carter，B. Batlogg， R.

J. Cava， J. J. Krajewski， W. F. Peck， Jr.， and H. Takagi， Phys. Rev. B. 50， 4216

(1994).

[2.31] M. Grio瓜 D;Malterre， B. Dardel， J.-M. Imer， Y. Baer， J. Muller， J. L. Jorda， and Y.Petroff， Phys. Rev. B 43， 1216 (1991).

[2.32] K.-M. Ho， M. L. Cohen， and W. E. Pickett， Phys. Rev. Lett. 41， 815 (1978).

[2お]M. Aono， F. J. Himpsel， and D. E. Eastman， Solid State Commun. 39， 225

(1981).

48 REFERENCES

Chapter 3

Photoemission Study of

Chevrel-Phase Compounds

3.1 Overview

3.1.1 Physical Properties of Chevrel-Phase Compounds

Crystal Structures of Chevrel-phase compounds

One ofthe la喝estgroups of superconducti時 compoundsis Chevrel-phase [3.1-5]， which

has the general formula AxM06X 8， where X stands for a chalcogen atom， namely S， Se，

or Te. The A atom can be any chemical element， such as alkali metal， alkaline earth，

simple metal， transition metal， noble metal， or rare earth [3.2]. As shown in the left

panel of Fig. 3.1， they have a rather remarkable structure called ‘Chevrel structure'

consisting of M06X 8 clusters which is shown in the right panel of Fig. 3.1. The cluster

is a somewhat deformed cube with eight X atoms on the cube corners and the six Mo

atoms at the centers of the cube faces forming an octahedron. As a whole， this cluster

and the A atom form a CsCl-type simple cubic lattice although the cube is somewhat

deformed， resulting in R3 space group. In addition， the M06X 8 clusters are rotated "，，25

degrees around the (111) axis and thus leave space in which the A atoms are located.

Large cations (A = Ag， In， Sn， Pb， etc.) are situated at the center between eight M06X 8

clusters to form nearly stoichiometric compounds， whereas small cations (A = Fe， Co，

Ni， Cu， etc.) occupy up to four of the twelve tetrahedral interstices available， resulting

in non-stoichiometric compounds [3.2]. In this work， we have studied compounds with

A = Sn and X = Se， corresponding to the former case. To understand the position of

49

50 CHAPTER 3. CHEVREL-PHASE COMPOUNDS

the large cation A in the crystal， it rnay be of interest to look at the structure from

another standpoint of view. In Fig. 3.2 is shown the projection of the crystal on the

hexagonal (1120) plane [3.6].

3

o{~: • Mo

Figure 3.1: Crystal structure of AM06X s・ Inthe left panel， we show the M06X s

cluster [3.4].

Superconductivity

The large portion of the Chevrel-phase compounds show superconductivity. The re-

markable features of their superconductivity are their relatively high critical tempera-

tures (Tc) for interrr附 alliccompounds and very high critical fields (HC2)' Some ofthem

are listed below in the Table 3.1 [3.2， 7] with their electronic specific heat coe伍cient

(γ) [3.8]. Although the Tc's are less than that of Nb3Sn， one of the A15 cornpounds，

with Tc = 23 K， the critical field of PbM06SS had been the highest until the cuprate

Sl収 rconductorswere discovered in 1986. Table 3.1leads us to the γーTcplot [3.9] again

出 wehave already discussed in Sec. 2.1.1. The Chevrel cornpounds are found to be in

the sarne region回 theboro・carbidesand the A15 compounds although the regions are

shifted frorn group to group.

3.1. OVERVIEW 51

Figure 3.2: View of the projection of the Chevrel structure on the hexagonal (12芝0)

plane [3.6].

Table 3.1: Collection of Tc， HC2 and γ'sof some Chevrel-phase compounds [3ム可.N ote that the reported values are somewhat scattered among the literature.

1 Compound~ 11 Tc _(K) .1 HC2 ('!2Jγ(mJ /mol __ K2) I

PbM06Sa 12.6-14.4 50--60 105-125

SnM06Sa 11.7-13.4 34-36 79-84

M06Sa 1.6 28

PbM06Sea 6.7 50

SnM06Sea 6.8

Mo6Sea 6.2-6.3 8.6-16.5 21-75


Band-Structure Calculations

The rernarkable superconducting properties described above are supposed to be due to

the high density of states (DOS) of conduction electrons essentially of Mo 4d character，

which has been confirrned by a nurnber of band-structure calculations by using the tight-

binding rnethod [3.10] or the local density approxirnation (LDA) [3.11-14]. Because the

Chevrel structure has 14-15 atorns in the unit cell accornpanied by the distortion and

rotation described above， the calculations were perforrned with sorne lirnitations. For

exarnple， Bullett performed it in a sirnplified localized-orbital calculation [3.11]. Nohl

et α1. calculated for real crystal structures althOlゆ notself-consistent [3.14]. Here，

the result by Freernan and J a山 orgfor SnM06Se8 [3.13， 15] is shown in Fig. 3.3. Their

calculation was done self-consistently but for a sirnplified structure with un-distorted

Mo octahedra and with a rhornbohedral angle of 900， because including the distortion

rnakes rnost of the 15 atorns in the unit cell inequivalent. In the sirnplified structure，

there is one A sites， six equivalent Mo sites and two types ofchalcogen sites. The rnethod

of the calculation was linear mu血n-tinorbital method (LMTO) with Hedin-Lundqvist

treatrnent of exchange and correlation.

One of the characteristic features is the high DOS near the Fermi level (EF) alrnost

rnainly due to fiat bands of Mo 4d character， which favors a high Tc. In fact， the Ferrni level is situated near Van Hove singularities [3.12]. In addition， the fiat bands rnean a

low Ferrni velocity which leads to a high critical magnetic field (HC2). At the sarne tirne

the result irnplies tirne that a large arnount of charge transfer from the Mo to chalcogen

sites and from the A site to the cluster.

In spite of the sirnplicity of the methods， a molecular-cluster approach is favored

to be as a good first approxirr凶 ion[3.13]， refiecting the localized nature of the Mo 4d

electrons within the cluster. We will analyze our spectra mainly based on the results of

Ja山 organd Freeman [3.13] hereafter， because， to the best of our knowledge， only their

band-structure calculation covers a wide energy range of valence band for SnMo6Se8・

Nevertheless other band-structure calculations for di旺erentA atorns would lead us to

essentially the same result as discussed below.

53 3.1. OVERVIEW

Sn 5sp

Mo4d

Se4p

5~SnMo6Sea l

Total

nu

で

(=oozcコa〉

O)ωov冊目ω』

ohv一ωcoo

10

O

5

O

O

-5 O 5 Energy (eV)

10 O 15

Figure 3.3: Band-structure DOS for SnMo6Se8 [3.15].


3.1.2 Motivation

Photoemission spectroscopy is one of the rnost useful rnethods to investigate the elec-

tronic states of solids. For the Chevrel-ph錨 ecompounds， there have already been

reported a nurnber of photoernission studies on them. The earliest work was reported

by Ihara et al. [3.16]. Kurn蹴 vet al. [3.17] reported the results of x-ray photoemission

spectroscopy (XPS) and x-ray emission spectroscopy (XES). After their reports， other

studies have been reported [3.18-22]. Although the obtained valence-band spectra were

cornpared with the band-structure calculations and good agreement was obtained be-

tween experiment and theory [3.17， 18]， the experiment has not been performed using

high enough resolution to study the electronic structure near Ep. In this chapter， we

will report on a photoemission study of Mo6Se7.5 and Sn1.2M06Se7ふIl).embersof the

Chevrel phase cornpounds， induding the result of high-resolution photoemission spec-

troscopy. Firstly， in Sec. 3.3.1， we will report on the result of the core level spectra and

will discuss their shifts between both cornpounds. Secondly the result of their valence四

band spectra will be shown. Thirdly we will compare the obtained spectra with the

band-structure calculations and propose a rnodel of the density of states to explain the

differences of the spectra between both rnaterials. The influence of the intercalation of

Sn into the Mo6Se8 clusters will be discussed. In addition， the inverse-photoemission

spectroscopy spectrum for Mo6Se7.5 will be reported.

3.2 Experiment

3.2.1 Sample Preparation

Mo6Se7.5 and Sn1.2M06Se7.5 were prepared as follows. For Mo6Se7ふ thernixture of Mo

and Se with the desired ratio was sealed in an evacuated silica tube， and then was

heated from 2000C to 9000C in a rate of 1000Cjhour， followed by anneali時 at9000C

for 12 hours. The product was ground and pressed into a pellet， and then was annealed

at 12000C for three days. For Sn1.2M06Se7・5，the mixture of the desired ratio of Sn，

Mo and Se powders was heated in an evacuated silica tube at 2000C for 12 hours and

2500C for 12 hours， and then was heated up to 8000C in a rate of 1000Cjhour， followed

by annealing at 8000C for 24 hours. The product was pressed into a pellet and was

annealed again at 10000C for a week. X-ray diffraction patterns of both sarnples were

successfully analyzed on the basis of the Chevrel structure [3.23]. The hexagonallattice

3.2. EXPER1MENT 55

parameters were determined to be α= 9.568 and 9.521 A and c = 11.180 and 11.838 A

for M06Se7.5 and Sn1.2M06Se7ふ respectively.The SnxM06Se8 compounds are stabilized

when the atomic ratio between Mo and Se is slightly non-stoichiometric. This non-

stoichiometry occurs due to the Se deficiency rather than excess Mo and moreover the

defects of Se are not supposed to be in ordered phase [3.23].

Preliminary resistivity data are plotted in Fig. 3.4. Transitions to superconductivity

are clearly seen at 5-8 K for M06Se7.5 and 2-8 K for Sn1.2M06Se7.5・

1.5 Mo6Se7.5

Sn1.2Mo6Se7

2.0x10・3

(εoq)b一〉詰

ω一一ωφ広

O

1.0

0.5トr

5 10 15 20 Temperature (K)

0.0 O 50 100 150 200 250

Temperature (K)

Figure 3.4: Resistivity of Mo6Se7.5 and Sn1.2M06Se7.5・ Inthe inset is shown the resis-

tivity around Tc.


3.2.2 Photoemission Measurement

XPS and ultraviolet photoemission spectroscopy (UPS) measurement were performed

for M06Se7.5 and Sn1.2M06Se7.5・XPSmeasurements were performed using the Mg Kα

line (hν= 1253.6 eV) and photoelectrons were collected using a double-pass cylindrical-

mirror analyzer. UPS measurements using the He 1 and He 11 resonance lines (hν= 21.2

eVand 40.8 eV， respectively) were made using a hemi-spherical analyzer. Calibration

and estimation of the instrumental resolution were done using Au evaporated on the

surface of the samples after each measurement. They were performed for XPS by

defining Au 4h/2 = 84.0 eV， and for UPS by measuring the Fermi edge. The total

resolution was "，1 eV， "，35 meV and "，80 meV for XPS， He 1 UPS， and He 11 UPS， respectively. The XPS measurements were made at liquid-nitrogen telllperature， and

the UPS measurements at "，28 K. The samples were scraped in situ with a diamond

file. During the XPS measurements， the intensity of the 0 ls core-Ievel signal， which

indicates surface contaminations on the samples， did not increase for several hours，

once it had been almost removed. Therefore the measurements were undertaken with

scraping the samples every several hours. Scraping were， however， done more frequently

for the UPS measurements because UPS were more surface-sensitive than XPS.

For M06Se7ふ inverse-photoemissionor Bremsstrahlung-isochromat spectroscopy (BIS)

was also done at liquid-nitrogen temperature. Calibration and estimation of the resolu-

tion were done as for UPS and the total resolution was determined "，1 eV. The sample

was scraped with a diamond file every several hours. The measurement conditions were

listed in Table 3.2.

Table 3.2: Conditions of the measurements for the Chevrel-phase compounds. LNT

stands for liquid-nitrogen temperature.

Measurement Photon Energy (e V) Resolution (FWHM) Temperature

He 1 UPS 21.2 "，40 meV "，30 K

He II UPS 40.8 "，80 meV "，30 K

XPS 1253.6 "，1 eV LNT

BIS 1486.6 "，1 eV LNT



3.3.1 Core Levels

We performed XPS measurements for Mo6Se7.5 and Sn1.2Mo6Se7.5 to obtain the Mo

3p， Mo 3d， Se 3p and Se 3d core level spectra of both compounds. The results are

shown in Figs. 3.5， 3.6， 3.7 and 3.8 with a solid line and a dashed line for Mo6Se7.5

and Sn1.2Mo6Se7ふ respectively.For Sn1.2Mo6Se7ふ wealso measured Sn 3d core level

spectrum shown in Fig. 3.9. In each figure， the peak positions determined by the

line-shape fitting are marked by vertical bars (see Table 3.3 below).

(ωzcコ.2』何)hv

一ωcgc一

Mo6Se7.5

Sn1.2Mo6Se7.5 XPS

Mo3d

‘

』甲• • • • • • • • • • • • •

‘

• • • • • • •• • • • • • • • • • • ・・・


220

Figure 3.5: Mo3d core唱 levelspectra of Mo6Se7.5 and Sn1.2Mo6Se7.5・

Their line shapes were analyzed by means of the least-square fitting. It is assumed

that each level has Mahan 's asymmetric line-shape reflecting the effect of screening

of a core hole by conduction electrons in the metallic solids [3.24]. The line shape is

convoluted with Gaussian and Lorentzian function which represent the instrumental

resolution and the core-hole lifetime broadening， respectively. Mahan's asymmetric

line-shape is expressed as follows (回 afunction ofωwhich is the kinetic energy of the

photoelectrons measured from the core-Ievel energy)

I(ω)=土 iLO(一ω)，r(α) Iω/cl

(3.1)


ωZCコ.2』何

Mo6Se7.5

Sn1.2Mo6Se7.5 XPS

Mo3p


380

Figure 3.6: Mo 3p core-level spectra of Mo6Se7.5 and Sn1.2M06Se7.S'

RJV

『

f

5e

一7S

円

U

a

u

sb

au，JV

oJ

M

1

nH nb

(ωzcコ.2」何)診一

ωcoFC

XPS

Se3d


45

Figure 3.7: Se 3d core-level spectra of Mo6Se7.5 and Sn1.2M06Se7.5・

59

Se3p

RESULTS AND DISCUSSIONS

Mo6Se7.5

Sn1.2Mo6Se7.5

3.3.

(ωzcコ.2』

MW)b一ωcgc一 155 170 165 160

Binding Energy (eV) 175

Figure 3.8: Se 3p core-level spectra of Mo6Se7.5 and Sn1.2Mo6Se7.5・

nU

M」伺

a'

ー

が

・・ゅ-am-.

Rd

・-----

マ，az--‘

lep--jJ

c

u

J

・・rJ:

a

u

s

r

・

n

u

-

-

パ・

M

M

2

・ぺ

tn

S

・叫

市

Sn3d (ωzcコ.2』何)hAH

一ωcsc-


よ -

500

Figure 3.9: Sn 3d core-Ievel spectra of Sn1.2Mo6Se7.5・


where c is the cut-off parameter with a magnitude of the order of the Fermi energy and

αis called singularity index， which characterizes the degree of asymmetry， given by

α= 2L(2l + 1)(生)2=Z-2L12(2l + 1)"

(3.2)

Here， ql is the charge of the conduction electrons with angular momentum 1 which

screens the core hole and 81 is the phase shift， where Friedel's sum rule holds:

Z=2午(2l+吟)=午ω (3.3)

Here， Z is the total charge which screens the core hole and， therefore， is identical to unity

for photoemission. The singularity index αmay refiect the amount of charge which the

atom has as conduction electrons around it. Therefore， by estimating α， information

on the partial density of states (DOS) of that atom can be obtained. In the most

simplified case [3.25]，αn = (QnNn(EF))2 holds provided thatαn， Qn and Nn(EF) are

the asymmetric parameter， the valence-electron-core-hole Coulomb attraction energy

and the partial DOS at EF as to the n-site atom， respectively.

Based on those facts， we analyzed the line-shape of each core level. The results are

shown in Table. 3.3. In the table，ムEdenotes the energy splitting between 3P3/2 and

3pl/2 or between 3ds/2 and 3d3/2 due to the atomic spin-orbit interaction. For the Mo

3d core level， however， the analysis has some ambiguity because the Se 38 core level

overlaps the Mo 3d core-level spectra. In this case， the singularity index α， which is sensitive to numerical instability， cannot be determined. In sulfide compounds， the Mo

3d and S 28 core levels are nearly at the same position - but are distinguishable in

this case一部 isshown in Fig. 3.10 for comparison [3.18].

Singularity Index

It is clear from Table. 3.3 that the singularity indices of the Mo core level are larger

than those of Se core level. A similar result has been already reported by Fujimori et

al. [3.18] These observations indicate that the contribution from the Mo 4d is dominant

at Ep rather than that from Se， which is consistent with the band-structure calculations

predicting that the large charge transfer from Mo to Se occurs to make the compounds

metallic.

61 RESULTS AND DISCUSSIONS 3.3.

Table 3.3: Results of core-Ievelline-shape fitting.

Sn1.2Mo6Se7.S

Core Level Position ムE α Position !l.E α

Se 3P3/2 160.38 5.77 く 0.02 160.27 5.77 < 0.01

Se 3ds/2 53.91 0.91 rvO.05 53.78 0;88 "-'0.07

Mo3p3/2 393.87 17.52 rvO.18 393.67 17.52 rvO.18

Mo3ds/2 227.96 3.23 227.86 3.21 一

Mo6Se7.5

3d 512

Mo制Fel.2SMo6S7.汚

(ωLF-zコ・mgd『}

〉

LF-ωZωLFZ-zo-ωω-玄ωO」「

oza

226 234 230 BJNDJNG ENERGV (eV)

238

m other each to close located Figure

Fe1.2SMo6S7.7S [3.18]. This situation holds for our selenides.

are levels core 2s and S 3d Mo 3.10:

CHEVREL-PHASE COMPOUNDS CHAPTER 3. 62

Core Level Shi此s

That is，

each core level of Mo6Se7.5 hω0.1-0.2 eV higher binding energy (EBω) t凶ha印nt出ha叫t0ぱf

Sn町1

XPS spectra and Mo 18 absorption of various AxMo6XS compounds (A = Pb， Ni， Cu，

and so on and X = S， Se， and Te) to observe that the core-level shifts vary linear1y with

the intercluster Mo-Mo distanceωwell as the rhornbohedral lattice parameter. Their

Judging frorn Table. 3.3， systematic core-Ievel shifts are found to exist.

results of the core-level shifts are plotted against the intercluster McトModistance in

Fig. 3.11 with open circles. Our results are added in the figure with closed circles [3.26].

The points with a cross mark are for selenides and tellurides. The others are for sul-

fides. Although the data points are quite scattered， still there appears sorne correlation

between the inter-cluster McトModistance and the core-Ievel shift for the selenides and

tellurides. Our results seern to be consistent with the trend in that En increases as the

3.8

・〈

o g 36 ω て3

Q)

窃 3.4

~ I 3

~ 1+ 。3.22 0 2

3.0

Mo-Mo distance increases.

5十Mo 3P3I2 5+ Mo 3d5/2 『

午午+

ー

。。。000 十

ー

O

内

M

O

34φ

十

斗O

『

O

394.0 393.6 393.2 Binding Energy (eV)

O

ーO

228.0 227.6 227.2 Binding Energy (eV)

O

3.8

< ~ 3.6 s ω 匂

ei> 3.4 ω コι3 。芭 3.20 2 0

:2 3.0

Figure 3.11: Binding energies of the Mo 3d5/2 and the Mo 3P3/2 core level of various

Chevrel-phase cornpounds plotted against the Mo-Mo intercluster distance in the left

and right panel， respectively. The data represented with the open circles are reported

in Ref. [3.21]. Our data of Sn1.2Mo山 7.5and Mo6Se7.5 are shown with closed circles.

The cornpounds with a cross mark are Sn1.2M06Se7.5 (1)， Mo6Se7.5 (2)， Mo6Ses (3)，

LaM06Ses (4) and M06TeS (5). The others are sulfides.


Now， the reason should be asked why the systematic trend of the core-level shifts

occurs. The cause of the core-level shifts is in general not trivial， but it rnay be related

to the shift of the Ferrni level. Then，槌 afirst step， we rnay well assume that the

electronic structure of the Chevrel-phase cornpounds can be explained approximately

by that of the M06 cluster as discussed in Sec. 3.1.1. In addition， it is also described in

that section that a large amount of charge transfer occurs frorn the A site to the M06X8

cluster. Therefore， the total nurnber of electrons in the cluster increases when Sn is

added to M06Se7.5・ Hereif we postulate a sirnple rigid-band model for the electronic

structure of these compounds， the trend ofcore level shifts would be reverse when Sn is

doped. In fact， the Ferrni level would be pushed up by Sn・doping，and the EB of each

core level should increase in going from M06Se7.5 to Sn1.2M06Se7.5' This， however， does

not hold in this case. Based on these discussions， our results imply that the electronic

structure of the valence band itself is changed and behaves unlike a rigid band model

when Sn is added to the inter-cluster site of M06Se7.5・Thiswill be further discussed

below (see Fig. 3.15).

3ふ 2 Valence-Band Photoemission Spectra

Wehavemeωured the valence-band photoemission spectra of M06Se7.5 and Sn1.2M06Se7.5

at photon energies hν= 21.2 eV (He 1 UPS)， 40.8 eV (He II UPS) and 1253.6 eV (XPS).

The spectra covering a wide energy range of the valence band are shown in Fig. 3.12.

These spectra have been normalized to the peak height around EB "，，1.5 eV. We can

estimate the degree of the contribution of each constituent element according to its

cross-section. The discussion can be done as in Sec. 2.3.2. The trend of the cross-

sections per electron relative to Mo 4d is shown in Fig. 3.13 as a function of photon

energy [3.27].

Wide Range Spectra

Judging from all the spectra in Fig. 3.12， roughly three structures are distinguishable

in spectra of both compounds. Here， these structures are temporarily called A (from

o to "，，2 eV)， B (""3 eV)， and C (from "，，4 to ，，-，7 eV)槌 shownin the figure. Because

Sn 5s core level is observed at EB "-' 14 eV， we have only to take into account Mo

4d and Se 4p. The contribution of Mo 5s and Sn 5sp on the valence-band spectra is

negligible because of their small amount of electrons in these compounds and of their


(ωtcコ.0』何) He 11

hv = 40.8 eV hv

一ωcgc

Hel hv = 21.2 eV

|~I I~ c ~I

12 10 4 O 8 6 2

Binding Energy (eV)

Figure 3.12: Valence-band photoemission spectra of Mo6Se7.5 and Sn1.2M06Se7.5・


10

τ.....__.........一一一・........

---.._.i，.-----一

ベ〉ー Se4pート Mo5s-← Sn5p

.___..........+I'..oa. 一一--------+------------{コー Sn5s

一・-Mo4d

0.1

100 Photon Energy (e V)

nu nU

(coboω一ω』

ωa)O一芯江

cozooωωωO』

O

Figure 3.13: Cross-sections per electron of the atomic orbitals relative to Mo 4d [3.27].

relatively small cross-sections as are seen in Fig. 3.13. In addition， based on the fact

that the relative cross-section of Se 4p to Mo 4d is largest at hν= 1253.6 eV (XPS) and

smallest at 40.8 eV (He 11 UPS)， we can determine A to be of mainly Mo 4d character

which shows up as a distinct peak in the He 1 and He II UPS spectra.

way， structures B and C are attributed to Se 4p character because they appear as the

largest broad feature in XPS. In the XPS spectra， it is hard to discriminate between B

and C because of the low resolution or because of the different degree of hybridization

In a similar

between Mo 4d and Se 4p.

The structures seen at EB = 7-10 eV in the UPS spectra， which are especially

remarkable in Sn1.2Mo6Se7.S， might not be intrinsic since there is little signal of them in

the spectra of both compounds measured by XPS， which is empirically not so sensitive


to contaminations， and that the intensities of the structures are dependent on the

compounds.

The above assignment is qualitatively consistent with the band-structure calcula-

tions shown in Fig. 3.3. That is， Mo 4d character is dominant in the rather narrow

energy range from E B = 0 to "，2 e V and Se 4p character appearsωa broad band from

EB = 3 eVもo"，7 eV. Although the band-structure calculation has been made only

for SnMo6Ses邸 shownin Fig. 3.3， the calculation indicates that Mo 4d and Se 4p are

more hybridized around EB = 3 eV than EB = 4-7 eV. These positions correspond to

structures B and C， respectively， which indicates that both structures have qualitatively

different characters in their origin.

Comparison between Mo6Se7.5 and Sn1.2M06Se7.5

Figure 3.14 shows the XPS， He 1 and He 11 UPS spectra of both compounds from

EB = -0.3 to 4.0 eV which are normalized to their peak height.

It is obvious that the intensity of Sn1.2Mo6Se7.5 around EB = 1.0 eV is higher than

that of Mo6Se7.5・ Thisobservation holds for all the three spectra. Therefore， we may

state that the Mo 4d band of Mo6Se7.5 is shifted to higher binding energy compared

with that of Sn1.2M06Se7.5' This observation is apparently inconsistent with the rigid-

band model， according to which the addition of Sn would raise the Fermi level and

thus would lower the Mo 4d band relative to E F・ Wewill argue below that the band

structures themselves are different between the two and that to determine the amount

of this shift is not simple. We propose that shifts of the core-levels and the valence-band

between Mo6Se7.5 and Sn1.2M06Se7.5 are explained by the narrowing of the Mo 4d band

due to the increase of the distance between Mo6X s clusters. When the X atom goes

from S to Se， the lattice parameters increase because of the larger atomic radius of Se.

In a similar way， by inserting large atoms such as Sn and Pb， the distance between

the clusters increases. This results in the decrease of the Mo 4d bandwidth， and in

turn lowers the position of the Fermi level relative to the other core and valence levels

because the Fermi level is located close to the top of the Mo 4d band. This can be

pictured in Fig. 3.15. It should be emphasized here that the decrease of the Mo 4d

band width was predicted in the band-structure calculations by Bullett [3.11]回 shown

in Fig. 3.16. The Mo 4d bandwidth surely decreases in going from Mo6SS to Mo6Ses

and from Mo6Ses to SnMo6Ses・


......・.・・.-・.. ・..... • . . . . -. . . . . ‘ . . . ‘ . . . . . . . . . . . . . .

XPS

He 11

:.......-----.‘・. . 、. . . • . . . . . • . . . . . ‘ . . . .

‘ . . . . ‘ . .

〆，t

dF

、司、

hw 、・『

h

ペ

晶.、

Hel

Mo6Se7.5 …・ Sn1.2Mo6Se7.5

(ωzcコ.2』伺)会

ωcsc-

O 2 1 Binding Energy (eV)

3 4

Figure 3.14: Valence-band photoemission spectra of Mo6Seu and Sn1.2Mo6Se7.5 from

EB=ー0.3to 4.0 eV.

68

Figure 3.15:

Sn1.2 Mo6Se7.5・

CHAPTER 3. CHEVREL-PHASE COMPOUNDS

Mo6Se7.5

Sn1.2Mo6Se7.5

Schematic

3.0

2・0

【

ミ 1.0・4E 。・4• 4 z ~ g ，. a ::: ....0 ・m.. -• -凶 3・0

2・0

Se4p

change of the

1 111 1111 111 1111

11目11111 1111111111

M、Sa

PbMo_S 't5 ~a

EF valence band in going from Mo6Se7.5 to

PbM"I;Sea

Figure 3.16: Band-structure DOS calculated by Bullett [3.11].


He 1 UPS spectra measured within the range of 300 me V of the Fermi level are shown

in Fig. 3.17. They are normalized in the same way as done in Fig. 3.14. They show

featureless spectra although the band-structure calculations [3.10] predict the presence

of narrow d-type conduction bands. Comparing the both spectra， the intensity at EF

is higher in Mo6Se7.5 than in Sn1.2M06Se7.5・ Thismight reflect the superconducting

critical temperatures (Tc) which is higher in the former compound than in the latter

compoundωseen in Fig. 3.4. We must， however， be careful in this type of discussion

because Tc is a subtle physical parameter dependent not only on the DOS at EF but also

on the electron-phonon coupling strength. To add to this， the photoemission intensity

is proportional not only to the state intensity of quasi-particles but also to the spectral

weight of the quasi-particles (the residue of the one-particle Green's function). In fact，

it was reported th抗 Tc'sare almost same in both compounds [3.3] (see Table. 3.1).

(ωzcコ.0』何

)

Hel

b

~ 11・Mo6Se7.5さ110 Sn1.2Mo6Se7.5

0.20 0.10 0.00 ー0.10

Binding Energy (eV)

Figure 3.17: Valence-band photoemission spectra of Mo6Se7.5 and Sn1.2M06Se7.5 near

EF.


Fine Structures in the UPS Spectra of Mo6Se7.5 and Sn1.2M06Se7.5 near Ep

Judging from Fig. 3.14， the spectra seem to have many fine structures refl.ecting the

electronic band structure of each compound. In order to detect fine structures qu柏田

titatively， the derivative-spectrum technique has been usually used. In this method， a

measured spectrum is twice differentiated回 tobinding energy， and then a fine structure

appears as a hollow in the second-derivative spectrum.

The result is given in Fig. 3.18 for Mo6Se7.5 and Fig. 3.19 for Sn1.2M06Se7.5・ In

each figure， the He 1 and He II UPS spectra are plotted with a dashed and solid line，

respectively. The second derivative spectra were smoothed appropriately after differ-

entiation. Comparison between the results of both He 1 and He II UPS differentiated

spectra guarantees our discussion below. In fact， as far回 theregion of tinding energy

between 0 and 2 e V is concerned， the differentiated spectra of He 1 and He II UPS have

surprisingly strong correlation between them. The steep behavior at EB = 0.0 eV is due to the Fermi distribution function. On the contrary， they have weaker correlation

between ，，"，2 and ""'2.5 eV， where positive structures can be seen in the differentiated

spectra corresponding to broad dips in the original spectra. No remarkable correlation

seems to exist in the region EB 三3e V. These facts refl.ect the ratio of hybridization and

cross sections between Mo 4d and Se 4p atomic orbital. lndeed， the strongly correlated

region indicates the presence of dominantly Mo 4d character and the un-correlated

region the broad Se 4p character.

Although the structures have some correspondence between each other， their posi-

tions and intensities are essentially different between Mo6Se7.5 and Sn1.2M06Se7ふ which

directly refl.ects the di旺"erencesin the band structures. The positions of the structures

marked a-d and α'-d' for Mo6Se7.5 and Sn1.2M06Se7.5 in the figures， respectively， are

listed below in Table 3.4.

Table 3.4: Positions (eV) of the fine structures of the He 1 and He II UPS spectra.

α b C d

Mo6Se7.5|0.2 0.6-1.0 1.1-1.3 1.5-1.8

α' b' d d'

Sn}州 6Se7.5|0.4 0.8-1.1 1.2-1.4 1.6-1.8

71 RESULTS AND DISCUSSIONS

|Mo6Se7.51

3.3.

Original Spectra

..‘、.・-，_..- .#..'.・.... 司、.'.. ..'司.司、・・--...・・w・... ・' ‘・.-・・.".・・・・.- ・.‘・・-..、.-..#、- ・. . ・.. . ‘ . . . . . .

‘ .. . . . . • • ・、.-1・.・0--. -t¥ ・‘‘ !a .

Hel He 11

(ωZCコ.2』何)hAV

一ωcsc

Second Derivative Spectra


4

Figure 3.18: Second derivative spectra of Mo6Se7.5 and the original ones. The dashed

and solid lines represent the He 1 and He 11 UPS spectra， respectively. The a-d indicate

the structures of which positions are listed in Table 3.4， whereas the dashed vertical

line indicates a distinct dip structure.

CHEVREL-PHASE COMPOUNDS CHAPTER 3.

|Sn1.2Mo6Se7.51

72

Original Spectra

、ー.'---..、.、'.... "'.，..............・

-、

九J1.

11 、.・. ¥

・.‘.・

lh

Nj

a'

Hel He 11

(ωtcコ.2」何)会

ωcgc一

Second Derivative Spectra

O 2 1 Binding Energy (eV)

3 4

Second derivative spectra of SnL2Mo6Se7.5 and the original ones.

dashed and solid lines represent the He 1 and He 11 UPS spectra， respectively. The α'-d'

The Figure 3.19:

indicate the structures of which positions are listed in Table 3.4， whereas the dashed

verticalline indicates a distinct dip structure.


BIS Spectra 3.3.3

For Mo6Se7ふ inverse-photoemissionor Bremsstrahlung-isochromat spectroscopy (BIS)

measurement was performed. The result is shown in Fig. 3.20. The main peak around

2 eV above EF is easily assigned to Mo 4d character， because Mo 4d has a large density

of unoccupied states and its cross-section is larger than the other components such as

Se 4p. The broad structure above 6 eV is of Mo 4p character.

A characteristic feature is a shoulder at "，1 eV above Ep as shown by an arrow

All the band-structure calculations [3.10-14] predicted the existence of in the figure.

an energy-gap around 1 eV above Ep・

below this gap. Therefore， the intensity from Ep to 1 eV above EF correspond to the

contribution of the lower Mo 4d band.

As a result， the Fermi level is situated just

• 、、vJWMM

BIS 1486.6 eV hv=

-h

、a-'

a可.

.

，

•• |Mo6Se7.51

.. ，・i.. e・・

(ωzcコ.2』何)会

ωcgc一，

10 8 、‘.E''v

e

，，a・、、

6

F

E』0

.，E‘

e

4N

4E・‘a

e

R

2mw

FE e

n

E』

nU

-2

Figure 3.20: BIS spectrum of Mo6Se7.S. The arrow indicates the dip around 1 eV above

EF.



In this section， qualitative comparison between the photoemission spectra and theoret-

ical spectra derived from the band-structure calculations. We have adopted the result

for SnMo6Ses of Freeman and Jarlborg [3.15]， because for Mo6Ses there is no calcula-

tion available covering a wide energy range of the valence band. Nevertheless， Nohl

et al. [3.14] have reported their間 sultof the band-structure calculation for Mo6Ses for

a very narrow range of "，0.3 eV around Ep， which will be compared with our high

resolution He 1 UPS spectrum for Mo6Se7.5・

In comparing the experiments with the band-structure calculations， it is necessary

to re-define the Fermi level of the calculation， because Sn1.2M06Se7.5 h邸1.4electrons

(0.2 x 2 + 0.5 x 2) more than SnMo6Ses・Thenit is needed to shift the， Fermi level by

this amount of electrons in the band-structure calculation by the following operation.

Because the Se defects are not supposed to be in the ordered ph部 e，this shift of the

Fermi level is justified. For Mo6Se7.5， the Fermi level was also shifted by the amount of

lack of 1 electron ((ー2)x 1 + 0.5 x 2) in the calculation for SnMo6Ses・

To obtain the theoretical spectra from the band-structure calculations， we have

broadened the calculated DOS as was done in Sec. 2.3.5. According to Figs. 3.3 and

3.13， we have only to take into account the contribution of Mo 4d and Se 4p. Both

have been weighted by the corresponding photoionization cross-sections at each photon

energy， and this weighted DOS has been broadened by convoluting with a Gaussian

and a Lorentzian which represent the instrumental resolution (see Table 3.2) and the

lifetime broadening， respectively. We assume that the lifetime width is linear in energy

E measured from Ep， i.e.FWHMω=αIE-Epl. The coe伍cientα，which phenomenか

logically represent the intensity of the lifetime of the photかholewi th increasing binding

energy， is a parameter which is determined so as to well reproduce the measured spec-

tra. For both compounds we have taken α= 0.24 and 0.40 for the photoemission and

inverse-photoemission spectra， respectively. In simulating the spectra， we have also

added an integral background due to secondary electron ernission as shown by dashed

lines in the figures.

Comparison for Whole Valence-Band Spectra

Figures 3.21 and 3.22 show cornparison between the theoretical photoemission spectra

derived from the band-structure calculations and the measured XPS， He 1 and He 11 UPS


spectra for Mo6Se7.5 and Sn1.2Mo6Se7ふ respectively.Note again that the theoretical

spectra are only for SnMo6Ses， although the Fermi level has been shifted appropriately.

The theoretical spectra have been normalized to the intensity of the Mo 4d compか

nent. Roughly two structures are seen in theoretical spectra are seen at EB = 0-2 eV and EB = 3-7 eV， respectively. The former corresponds to the non-bonding Mo 4d

component and the latter to Se 4p partly hybridized with Mo 4d. It is clear from the

figures that the calculated Se 4p band well reproduces the photoemission spectra for

both compounds except for the shift of "'0.5 eV away from Ep. Then， it is obvious

that the broad Se 4p band exists between "，3 and "，7 eV.

Large discrepancies， however， appear between Ep and "，3 eV. The structure mainly

of Mo 4d character are shifted by "，1 eV to .higher binding energies. As a result， in

the measured spectra of XPS， the separation between the Mo 4d baIld and the Se

4p band， which can be seen in theoretical spectra， becomes obscure. The separation

between the Mo 4d and chalcogen X p bands is a clear conclusion of many band calcu-

lations [3.10-14]. For example， in Fig. 3.23 [3.18]， the 1附.suredand theoretical spectra

for Fe1.3Mo6S7.9 are shown. The separation in the measured spectra is larger than in

our selenides， which is qualitatively consistent with the result of the band-structure

calculations， although the theory plotted in Fig. 3.23 predicts larger separations than

in the present c部 e.

Comparison with BIS Spectrum

We have made comparison between the theory and experiment錨 tothe unoccupied

state of Mo6Se7ル Theresult is shown in Fig. 3.24. The structure above 6 eV is of

Mo 4p character in the experimental spectra whereas the Mo 4p partial DOS is not

included in the theoretical spectra. The peak around 2.5 e V corresponds to the Mo

4d unoccupied states of which position the theoretical spectrum well reproduces. On

the contrary， the experimental intensity around 1 e V where the dip between the Mo d

bands exists is different from the theoretical one.

Comparison with Spectra near Ep

The spectra near Ep are also compared with the theoretical spectra. The results are

shown in Figs. 3.25 and 3.26 with the Mo 4d partial DOS of which the Fermi level

has been shifted appropriately. The notation a-d and a'-d' for the structures in the


XPS hv = 1253.6 eV

|Mo6Se7.51

(ωtcコ

.........................................._--ー・・・・.・・・・ー-一ー・・・--・--ー・・・・・・・・・・・・・・・・・・・ー-一ー・・・・-.

• 2」何

一.....一一一一一一ー・・・・・ー・・・ー一・・・・・・・・・・・-

-・・・・・ー-.-ー・・・・・・・・・・-

-・・.・・-『司・---. . . . ‘・一・.、. 、. . 、、

‘

He 11 hv = 40.8 eV

、句圃〆

会ωcovc

Hel hv = 21.2 eV

• Photoemission Band Calculation Background

10 8 4 O 6 2

Binding Energy (eV)

Figure 3.21: Comparison of the XPS， He 1 and He 11 UPS spectra (dots) of Mo6Se7.5

with the theoretical spectra derived from the band-structure calculations of SnMo6Ses

(solid curves) [3.15]. The dashed lines show the integral background.


XPS hv = 1253.6 eV

|Sn1.2Mo6Se7.51

(ωzcコ.0』何)会

ωcsc-

He 11 hv = 40.8 eV

Hel 的 =21.2 eV

• Photoemission 8and Calculation 8ackground

10 864 2 8inding Energy (eV)

O

Figure 3.22: Comparison of the XPS， He 1 and He 11 UPS spectra (dots) of Sn1.2Mo6Se7.5

with the theoretical spectra derived from the band-structure calculations of SnMo6Ses

(solid curves) [3.15]. The dashed lines show the integral background.

CHEVREL-PHASE COMPOUNDS CHAPTER 3. 78

1253.6 eV

CROSS SECTlO仲 MODULATED

DOS -NOHl. KlOSE 1:;"<< BG

& ANDERSEN ーーーーーーーーーー』

Fel.3Mo6S7.9

‘ 』

BUllETT

{凶」

F-Z2.国gd『)〉」

F-凶Z凶ト

z-zo-凶的

-Z凶OLFoza

。12 8 4 BINDING ENERGY (eV)

16

for Figure

Fe1.3M06S7.9 [3.18]. Theoretical spectra were derived from various band-structure cal-

culations listed on the figure [3.11， 13， 14].

spectra band valence XPS theoretical and measured The 3.23:

We experimental spectra are the same as those in Figs. 3.18 and 3.19， respectively.

have also marked the prominent structures in the theoretical spectra with x-z.

In both compounds， the position of the dip located between "，2 and "，2.7 eV is con-

sistent with the theoretical spectra. This dip corresponds to the separation between the

Mo 4d band and Se 4p band. Therefore， the following comparison will be concentrated

on the structures between EF and "，2 eV， where the contribution of the Mo 4d band

is dominant.

At first glance， in Fig. 3.25， we are apt to assign αto x， b and c to y and d to z.

Such assignment is， however， inconsistent with the relative intensities of the structures.

As is discussed above， the center of gravity of the Mo 4d band has been shifted by

"，1 eV toward higher binding energies when compared with the theory. This makes


|Mo6Se7.sl • Photoemission 一一 BandCalculation

Background

BIS hv = 1486.6 eV

(ωzcコ.D』伺)抗日一

ωCOHC一

ー2 0 2 4 6 8 Energy Relative to EF (e V)

Figure 3.24: Comparison between theoretical and experimental BIS spectra of

Mo6Se7.5 [3.15).

the assignment di伍cult，but the same also holds for Sn1.2Mo6Se7.5 (see Fig. 3.26). If

the assignment above were right， the structure c (d) and d (d') would be too intense.

Otherwise， if the spectral weight did transferred to higher binding energies and the

structures could be assigned， for example， b (b') to x and c (c') to y， what would drive

these transfers?

Here， it is of interest to compare the spectrum in the very vicinity of Ep with the

theoretical spectra. In Fig. 3.27， we show comparison between the He 1 UPS spec-

trum for Mo6Se7.5 measured around Ep and the theoretical spectrum derived in the

same method from the band-structure calculations for Mo6Ses reported by Andersen et

al. [3.12). In Fig. 3.28， comparison between the He 1 UPS spectrum for Sn1.2Mo6Se7.5

and the theoretical spectrum is shown. This time， however， the theoretical spectrum has

been derived from the band-structure calculations for PbMo6Ses [3.12) because there


He 11 hv = 40.8 eV

|Mo6Se7.51

llTIll

円c門Hl

d

日円

C

コ.0』

C)

a 〉、

ω

室 Helcl 伽=21.2 eV

shifted partial DOS of Mo 4d

3.0 2.5 2.0 1.5 1.0 0.5 0.0 -0.5

Binding Energy (eV)

Figure 3.25: Comparison of He 1 and He 11 UPS spectra (dots) of Mo6Se7.5 with the

theoretical spectra for SnMo6Se8 (solid curves) [3.15]. The structure assignments are

the same shown in Fig. 3.18. 1n the bottom are shown the Mo 4d partial density of state

with the Fermi level shifted appropriately. For a more detail caption， see Fig. 3.21.


He 11 hv = 40.8 eV

(ωZCコ

a

yl円

ylHH

~dulHl

.2』何)

hv

一ωCOHC

Hel hv = 21.2 eV

.... .... -....... ..._-.... -. -. _...... -.. -_..... ...-...._-ー-一一ー・・・ー.・・・・・ー-一ー・・・ー・・・・......_........

shifted pa吋ialDOSof Mo 4d

3.0 2.5 2.0 1.5 1.0 0.5 Binding Energy (eV)

0.0 -0.5

Figure 3.26: Comparison of He 1 and He II UPS spectra (dots) of Sn1.2M06Se7.5 with

the theoretical spectra for SnMo6Ses (solid curves) [3.15]. The structure assignments

are the same shown in Fig. 3.19. In the bottom are shown the Mo 4d partial density of

state with the Fermi level shifted appropriately. For a more detail caption， see Fig. 3.22.


are no calculations available for SnMo6Ses in Ref. [3.12]. Nevertheless， both Sn and Pb

are divalent and moreover both SnMo6Ses and PbMo6Ses have almost the same lattice

constants [3司， which justifies our comparison between the experiment 0ぱfSn町1.2Mo匂6Se町7

and the band-structure calculations of PbMo句6Se匂s.Although the normalization between

the experiment and the theory cannot be performed because their results do not cover

the whole valence band， it is clear that the Van Hove singularities near EF are sup-

pressed or become obscured， which makes the experimental spectra featureless in this

reglOn.

(ωtcコ

• Photoemission 一一 TheoreticalSpectrum

一三

V

一e

-

e

一S'一12

-h-e1

一M

一lH2am

.2』何

、困層〆

hv一ωcovc

¥ shifted pa吋ialDOS

ofMo 4d

0.20 0.15 0.10 0.05 0.00 Binding Energy (eV)

-0.05

Figure 3.27: Comparison of He 1 UPS spectrum of Mo6Se7.5 and the theoretical spectrum

for Mo6Ses [3.12]. In the bottom are shown the Mo 4d partial density of state with the

Fermi level shifted appropriately.


• Photoemission 向Sn川11.2Mo6Se7.5Theoretical Spectrum .圃

.句.句......__ He I hv = 21.2 eV

----------・・--・..~

(ωtcコ

• • • • • • • • • • • • • 2』

MW)

、Ego-c

shifted oartial DOS of Mo 4d

¥ 0.4 0.2 0.0

Binding Energy (eV)

Fi思ue3.28: Comparison of He 1 UPS spectrum of Sn1.2Mo6Se7.5 and the theoretical

spectrum for PbMo6Se8 [3.12]. In the bottom are shown the Mo 4d partial density of

state with the Fermi level shifted appropriately.

In this way， large spectral-weight transfer toward higher binding energy by "，1 eV h錨

been observed in both compounds. One possible explanation is that this occlirs through

electron-electron correlation effect in the narrow d band， which have not been taken

into account in the band-structure calculations. In this depiction， the self-energy of an

electron may be regarded as being independent of an electron momentum k because

of the effective screening by conduction electrons. As a result， the observed band

structure becomes narrower than the band-structure calculations to form a coherent

structure， and the rest of the coherent part is transferred to an incoherent part as a

broad structure at higher binding energies. According to this picture， structures x， y

and z in the theoretical spectra would be observed in the experimental spectra錨 much


narrower structures near EF • Structures c (c') and d (d') could be assigned to their

incoherent part. This rnodel， however， does not explain the suppression of the spectral

intensity at EF unless the k-dependence of the self-energy is not taken into account in

the rnodel because the k-independent self-energy does not change the intensity at EF

(see Eq. (4.18) in Sec. 4.3). In fact， we have obtained featureless experirnental spectra

near EF， although the question always rernains whether our resolution of rneasurernent

"，，25 rne V is su伍cientto observe such narrow structures or not.

Another possible explanation is that the above phenornena rnight be due to the

electron-phonon interaction. As we will discuss below， the electron-phonon interaction

rnay rnake a significant infiuence on the photoernission spectra rneasured in the resolu-

tion of the order of 10 rneV. One of the rnain e証'ectsis the creation of satellites through

the rnulti-phonon ernission， which rnay lead to a substantial spectral weight transfer to

higher binding energies. The position and the intensity of the satellites strongly de-

pend on the strength of the electron-phonon coupling and the phonon frequency. Since

the average phonon energy in this cornpounds can be estimated to be at most "，，40

meV judging frorn the inelastic-neutron scattering rneasurernent [3.3]， however， only

electron-phonon interaction seems insu血cientto fully explain the discrepancies of the

order of electron volt between the experimental and the theoretical spectra.

Here， it rnust be ernphasized that the discrepancies do not seern ‘extrinsic'， because

the assignrnent of the structures has been performed through comparison between the

He 1 and He 11 UPS spectra for each cornpound. The transfer of spectral weight com-

pared with the band-structure calculations are observed in both kinds of spectra. To

the best of our knowledge， the above discrepancy rernains to be solved essentially.

3.4 Conclusion

We have perforrned a detailed study on the electronic structure of two Chevrel-phase

cornpounds， M06Se7.5 and Sn1.2M06Se7.5・TheXPS core-level spectra have revealed sys-

tematic core-level shifts arnong various Chevrel-phase cornpounds of which the change

of the Mo-Mo intercluster distances seems to be responsible. 1n this point， the valence-

band spectra have the sarne tendency unlike the rigid-band rnodel， from which we can

propose that the M06Se8 clusters become more separated by the intercalation of Sn，

which results in the narrowing of the Mo 4d bands. The singularity index of each core

level has been discussed and it is verified that the contribution of Mo is dominant at EF •

3.4. CONCLUSION 85

The valence-band photoemission spectra shows rich fine structures. The positions and

intensities are somewhat different between M06Se7.5 and Sn1.2M06Se7.5・Wealso com-

pared them with the theoretical spectra derived from the band-structure calculations

and large discrepancies especially for the Mo 4d band are found. The assignment of the

measured fine structures to the band-structure calculation is found to be not so simple a

problem. The origin of this phenomenon has been discussed qualitatively， and indicated

that the electron-electron interaction or electron-phonon coupling may be responsible

for this， although only one of the two does not clearly explain it. The comparison

between theoretical and experimental BIS spectra reveals qualitative agreement as to

the presence of the splitting structure of the Mo 4d bands， which the band-structure

calculations have predicted， in spite of the existence of the qualitative discrepancies.


References

[3.1] Supercondωivity in Ternαry Compounds Vols. 1 and II， edited byの.Fischer and

M. B. Maple， (Springer-Verlag， Berlin， 1982).

[3.2] S. V. Vonsovsky， Y. A. Izymuov， and E. Z. Kurmaev， S叩 erconductivity01 Tran・

sition Metals (Springer， Berlin， Heidelberg， New York， 1982)， pp. 418-431.

[3司の.Fischer， Appl. Phys. 16， 1 (1978).

[3.4] T. Ohotani， Jikken KIα，gaku Kouza Vol. 16 (Maruzen， 1993)， in Japanese.

[3.5] M. Ishikawa Gekkan Physics Vol. 4 No. 12， (Kaiyou， 1983)， in Japanese.

[3.6] R. Chevrel and M. Sergent， in Superconductivity in Ternary CompoundsVols. 1，

edited byの.Fischer and M. B. Maple， (Springer-Verlag， Berlin， 1982) p. 33.

[3.可M.Decroux andの.Fischer， in Superconductivity in Ternary CompoundsVols. II，

edited byの.Fischer and M. B. Maple， (Springer-Verlag， Berlin， 1982) p.57.

[3.8] F. Pobell， D. Rainer and H. Wuhl， p. 255 of Ref. [3.6].

[伊3.司H.'τT;、'akag副i，R. J. Cav，刊a，H.E日is鈍a叫.1札}

J. J. Krajewski， and W. F. Peck， Jr.， Physica C 228， 389 (1994).

[3.10] L. F. Mattheiss， and C. Y. Fong， Phys. Rev. B 15， 1760 (1977).

[3.11] D. W. Bullett， Phys. Rev. Lett. 39， 664 (1977).

[3.12] O. K. Andersen， W. Klose and H. Nohl， Phys. Rev. B 17 1209 (1978).

[3.13] T. Jarlborg and A. J. Freeman， Phys. Rev. Lett. 44， 178 (1980).

[3.14] H. Nohl， W. Klo民 andO. K. Andersen， p. 165 of Ref. [3.6].

87

88 REFERENCES

[3.15] A. J. Freeman and T. Jarlborg， p. 178 of Ref. [3.6].

[3.16] H. Ihara， and K. Kirnura， Jap. J. Appl. Phys. 17， Suppl. 17-2， 281 (1978).

[3.17] E. Z. Kurmaev， Yu. M. Yarmoshenko， R. Nyholrn， N. Martensson and T. Jarl-

borg， Solid State Cornrnun. 37， 647 (1981).

[3.18] A. Fujirnori， M. Sekita， and H. Wada， Phys. Rev. B 33， 6652 (1986).

[3.19] F. C. Brown， B. A. Bunker， D. M. Ginsberg， T. J. Miller， W. M. Miller， and E.

A. Stern， Phys. Rev. B 34 7698 (1986)

[3.20] S. Sl砂， K. Soda， T. Mori， M. Yarnamoto， K. Kitazawa， and S. Tanaka， J. Phys.

Soc. Jpn. 55， 2102 (1986).

[3.21] S. Y，叫onath，M. S. Hegde， P. R. Sarode， C. N. R. Rao， A. M. Umarji and G.

V. Subba Rao， Solid State Cornrnun. 37， 325 (1981).

[3.22] H. Namatame， K. Soda， T. Mori， M. FUjisawa， M. Taniguchi， S. Suga， K. Ki-

tazawa， and S. Tanaka， Jap. J. Apply. Phys. 28， L266 (1989).

[3.23] T. Ohtani， private cornmunication.

[3.24] S. Hu出 er，Photoelectron Spectroscopy (Sp巾 ger-Verlag， Berlin， 1994) p. 112; G.

K. Wertheim and P. H. Citrin， in Photoemission in Solids， edited by M. Cardona

and L. Ley (Springer-Verlag， Berlin， 1978)， Vol. 1， p.197.

[3.25] J. C. W. Folmer and D. K. G. deBoer， Solid State Comrnun. 38， 1135 (1981).

[3.26] R. Chevrel and M. Serge民 pp.61-83 of Ref. [3.6].

[3.27] J.-J. Yeh and 1. Lindau， At. Data Nucl. Data Tables 32， 1 (1985).

Chapter 4

Electron-Phonon Interaction and

Photoemission Spectra

4.1 Motivation

In recent years， the resolution of photoemission spectroscopy has been greatly improved

to reach the order of 10 meV， which corresponds to the energy scale of optical phonons

in solids. Therefore electron-phonon interaction is likely to affectphotoemission spectra

near the Fermi level (Ep) to some extent， whereas there seem to be only few experiments

to clariち，the infiuence of this interaction. For example， Knupfer et al. [4.1] reported the

photoemission spectra of Rb3C60 which showed several temperature-dependent satellites

near EF (Fig. 4.1) which are impossible to be explained by band-structure calculations.

They analyzed these satellites in terms of electron-boson coupling where ‘boson' means

a phonon or a plasmon.

As reported already in the previous chapters， there exist some discrepancies between

our photoemission spectra and the band-structure calculations. In YNi2B2C， the band-

structure calculations have a Van Hove Singularity mainly of Ni 3d character just at

Ep， whereas there seems to be no evidence of the existence of such a sharp peak at

E p as far as our photoemission study is concerned. We also performed photoemission

measurements for the Chevrel-phase compounds which were， as in the borcトcarbides，

predicted by the band-structure calculations to have a high DOS due to Mo 4d electrons

around Ep. However， the observed Mo 4d band structures around Ep， several of which

are c1early distinguishable (Sec. 3.3.2)， do not show good agreement with the band-

structure calculations， although the gross electronic feature is in some agreement with

89

90 CHAPTER 4. ELECTRON-PHONON INTERACTION

c:: 1¥ ¥ ヨ I•

」コ咽

〉、

ロ由

民

I~-' 、

1 0.5 0

Blndlng energy (eVI -0.5

Figure 4.1: Photoemission spectra of Rb3C60出 afunction of temperature [4.1].

the band-structure calculations. It is of great interest how the disagreement occurs.

In this chapter， we will discuss a possible explanation for these discrepancies near

EF through electron-phonon interaction. The electron spectral function including this

interaction has been extensively studied quite early by Engelsberg and Schrieffer [4.2]

for systems where Migdal's theorem is assumed to be valid. Although their result is

for the most simplified case， still the essence does not seem to be lost. In Sec. 4.2.1

the general theory as to the electron-phonon interaction in metal is reviewed. After the

result of Engelsberg and Schrieffer is introduced in Sec. 4.2.2， our result of the simple

model calculation based on their result will be reported in Sec. 4.3. The cause of the

disappearance of the DOS peak at E F will be proposed at the same time.

4.2 Basis of Model Calculations

4.2.1 Electron-Phonon Interaction in Metal

Here we review on electron-phonon interaction in metals and the electron-phonon cou-

pling constant入ina general way [4.3~5].

The matrix elernent Mpplνwhich represents the electron-phonon interaction in a

4.2. BASIS OF MODEL CALCULATIONS 91

metal is given as follows:

持'p'v=J帆 -p'，v.VV)ゆpd3T， (4.1)

whereらisthe electron wave function with its momentum p， v is the mode of phonon， f.

is the unit vector parallel to the polarization of phonon， and V is the crystal potential.

Then， the so-called spectral function of the electron-phonon interaction α2(ω)F(ω)，

where ωstands for the phonon frequency， is defined by the following integration over

the Fermi surface:

r d2ρ2p r dポ2p〆f f2柄αa2(いω)F川F尺(ω )片=I ~. l' I ε |陥g必必Lゐふ，匂JvJ VF J (21πrh)3w1v j uF

(4.2)

where

gPP'v = n

2Maωp-pvinpw v， (4.3)

and VF is the Fermi velocity， and A1a is the atomic mass concerned. It is known that for

metallic solids 9pp'v may be rewritten部 gqin terms of the momentum of the phonon

and the following holds:

gq cx:: q冨 (4.4)

The a2(ω)F(ω) given above is the average over the strength of the electron-phonon

interaction on the Fermi surface. Finally， a dimensionless characteristic parameter入，

which is called the electron-phonon coupling constant， is defined by

入=2 foWMO:t: a2(ω)ケ)

(4.5)

入isoften expressed using the averages of the matrix elements and the phonon frequen-

cles

入=(M;p'v)N(EF)

M(ω2) (4.6)

where N(EF) is the density of states at EF・Inthe most simplified case where only one

phonon frequency ωE is taken into account (Einstein model)，入 isreduced to

入_2g2N(EF) 一

ωE (4.7)

This expression is usually used in a number of theoretical model calculations in the

literature.


An electron on the Fermi surface is dressed with phonons through the electron-

phonon interaction， which leads to a mass enhancement of the electron by factor 1 +λ

Then the DOS at Ep (Nホ(Ep))of the phonon-dressed electrons is expressed as follows:

N事(Ep)= N(Ep)(l +入)， (4.8)

which means the enhancement of the electronic specific coeffi.cientγ. According to the

comparison between the transport experirnents and the band-structure calculations，入

is estimated入忘 1in usual cases.

4.2.2 Engelsberg&Schrieffer's Theory

Engelsberg and Schrieffer have given the expression of the electron self-energy in the

electron-phonon coupling systern. Here we surnrnarize part of their results.

The rnodel which they studied is:

冗 =LE2ckck +乞ωqbtbq+ L 9q(bq + b~q)cl+qCk ， (4.9)

where Ck (4) is an annihilation (creation) operator of an electron with the dispersion relation 1::2 and the bq (b~) is the counterpart of a phonon with the dispersion relation

Wq • The superscript 0 for 1::2 rneans the energy as a free partic1e which is not coupled

with phonons. They deduced their result on the limited conditions as follows:

• The electron Green's function is treated self-consistently whereas the phonon

Green's function is not.

• The energy of phonons is treated as being constant WE (Einstein modelり).The

rnat仕ri以xele目m悶1

phonon (q). (Although they have treated the case for Debye rnodel with 9qぽ ql/2，

we will not refer to them here for sirnplicity.)

. It is assumed that the Migdal's approximation holds which enabled them to treat

this problern in perturbation theory.

• Electron-hole syrnrnetry is assurned.

• The electron self-energy E (k， 1::) is treated as being independent of the momentum

k.

ノ

4.2. BASIS OF MODEL CALCULATIONS 93

• The density of states of electrons is assumed to be constant.

Based on these assumptions， they obtained for the electron Green's function and its

self-energy舗:

G(仰)=ー→」〆-f2 -E(k， f)'

where the k-independent self-energy E(f) is given by

and

Re E(f) =一;入ωEln件竺|~ It一ωEI

1 =-~π入ωEsgn(ε) for Ifl >ωE ImE(ε) <一

l = 0 for 1ε1<ωE

(4.10)

(4.11)

(4.12)

where λis already given in Eq. (4.7) (see Appendix A for detail). These two equations

are connected with each other by the Kramers-Kronig relation.

We can use this formula Eqs. (4.11) and (4.12)儲 astarting point to consider the

infiuence on the photoemission spectra of the electron-phonon interaction， although it

must be remembered that it is derived based on many assumptions.

4.2.3 Method of Calculations

The electron spectral function ρバ(f)is calculated in general as given i泊nSec 1.2

ρバ仲刷(恥ωεο)片=一; 乞ImG(伏k丸仰川，パεけ) .. k

( 4.13)

As far as the k-independent self-energy E(ε) is concerned， the above ρ( f) can be rewri t-

ten replacing d3 k by po (ピ)df':

p(ε) = 一一一πγf -e -E(ε)

ーかo(ピ)df'Im二 f-2{ピ'

(4.14)

(4.15)

where ρ。(f)is the density of states of the free electron refiecting only its dispersion

relation (f~) without electron-phonon coupling. By post山 tingthat po(ε) is constant

(Po(ε)三 ρ0)and the band is half-臼ledwith the band-width 2W to fulfill the condition

of electron-hole symmetry， we have only to calculate the following:

(W .L' 1mE(ε) ρ(ε) = 一一ρoI dt:' ムw--(ε-e-ReE(ε))2 + (ImE(ε))2・

(4.16)


Finally the following sum rule is worth noting:

4L

，α

、、，，J

EL

，，z‘、nu ρ

w

w

flム一一

6L

，a

、、，，F

4L

AY

∞

∞

fIIト

( 4.17)


We have obtained the spect凶 functionρ(f)by calculating Eq. (4.16) with changing

the two parameters， that is， the electron-phonon coupling constant入andthe Einstein

phonon frequency ωE， which are measured in unit of half of the band width W. The

results of the calculations for入=0.5， 1 and 2 are shown in Figs. 4.2， 4.3 and 4.4，

respectively， withωE/W = 0.01，0.1，0.3，0.6，1，3，6 and 50. The dashed lines in the

figures show ρo(ε) for comparison.入=0.5 correspo凶 tothe weak coupling condition

whereas入 =2 to the strong coupling condition.

It is clear from the figures that， when W >>ωE， the electron-phonon interaction

only broadens the original DOS ρ。(ε).In this case， the energies of most of the electrons

concerned are much larger than those of phonons and therefore interaction between

phonons and electrons result in the finite life-time of electrons 7r入ωE/2as given in

Eq. (4.12). This condition correspond to， for example， simple metals with wide s-

p band in which electron-phonon interaction apparently makes little infiuence on the

photoemission spectra.

On the other hand， when W <<ωE， which is not a realistic case， the main peak

becomes (1 +入)-1[4.2] times narrower than the original DOS ρ。(f)and the rest of the

spectral weight transfers to higher energies as incoherent part to fulfill the sum rule

Eq. (4.17).

When W and WE are of the same order， the spectral function is totally different

from the original DOS ρ。(ε)in tl凶 theadditional structures appear as incoherent

parts although the narrowed main structure exists close to them. In this case， many

electrons have almost the same energy as phonons， where quasi-particle picture is not

appropriate， as pointed out in Ref. [4.2]. We would like to emphasize here that this

situation is realistic enough in， for example， rnetals with narrow d bands near Ep. The

narrowing rate of the main structure around EF is (1十入)一1in this case， as in the

case of W<<ωE. This simplicity is due to the Einstein rnodel， where the electron with

its energy smaller than WE cannot damp as a phonon-dressed electron as seen in the

III時 inarypart of the self-energy (悶 Eq.(4.12)). Anyway， it is clear from the figures

¥

95

|λ= 0.51

RESULTS AND DISCUSSIONS 4.3.

C%/ W = 50

C%/W=6

C%/W=3

ω'E/W= 1 oa¥(ω)色 C%/ W = 0.6

C%/ W = 0.3

C%/ W = 0.1

C%/ W = 0.01

-10 -5 O Energy / W

5 10

Figure 4.2: Calculated spectral function with coupling constant入=0.5 for various

phonon frequencies ωE/W = 0.01，0.1，0.3，0.6，1，3，6 and 50. This入correspondsto the

weak-coupling. The solid and dashed lines show ρ(ε) and ρ。(f)， respecti vely.

ELECTRON-PHONON INTERACTION CHAPTER 4.

|λ= 11

96

ωE/W=50

~/W=6

~/W=3

~/W= 1 oa¥(ω)己 ~/W = 0.6

ωE/ W = 0.3

ωE/ W = 0.1

ωE / W = 0.01

ー10-5 O Energy / W

5 10

1 for various

The solid and dashed

Figure 4.3: Calculated spectral function with coupling constant入=

phonon frequencies ωE/W = 0.01，0.1，0.3，0.6，1，3，6 and 50.

lines show ρ(10) and ρo(ε)， respectively.

97

回

r.........・・・・・・吾..

RESULTS AND DISCUSSIONS 4.3.

C%/W=50

向 /W=6

C%/W=3

.. . . . . . . . . -....ー.........~~~_.~

f%/W=1

f%/ W = 0.6

oa¥(ω)a

C%/W=0.3

C%/ W = 0.1

ωE / W = 0.01

圃 10-5 O

Energy / W

5 10

Figure 4.4: Calculated spectral function with coupling constant入 2for various

phonon frequencies ωE/W = 0.01，0.1，0.3，0.6，1，3，6 and 50. This入correspondsto the

strong-coupling. The solid and dashed lines show ρ(E) and ρ'O(ε)， respectively.


that，ωthe coupling constant入increases，the spectral function differs more from the

original DOS.

Next we performed a calculation to obtain the photoemission spectrum with realistic

parameters， that is，入=2.6 and the phonon energy WE = 100 meV according to the

values estimated for LuNi2B2C [4.6]. The high frequency of phonon up to 106 meV is

reported to be due to a B-C bond stretching mode. The band width is set to 2W = 100

meV， which might well simulate the narrow band near Ep ofYNi2B2C mainly due

to Ni 3d character. The instrumental resolution (FWHM) 30 meV corresponds to

our experiment. The model photoemission spectrum obtained in this way is shown

in Fig. 4.5 together with the result without the electron-phonon coupling which was

obtained only by broadening the original DOS with the instrumental resolution. It is

clear that the intensity of the peak of the spectrum with the electron-phonon coupling

is less than half of that without electron-phonon coupling. This seems to be consistent

with the case of our high-resolution spectra of YNi2B2C (see Fig. 2.21)， where the

sharp DOS peak predicted by the band-structure calculations is observed to be strongly

suppressed in the measured spectrum.

It must， however， be noted here that the following holds for the k-independent

self-energy ~ (ε):

ρ(μ)=ρo(μ)， (4.18)

where μis the chemical potential of electrons defined by

μ-E2 -~(μ) 三 O. (4.19)

Here， as far as Eqs. (4.11) and (4.12) are concerned， we can regardμ 酪 Ep because

Re~(μ = Ep) equals O. Eq. (4.18) can be proved easily as follows using Eq. (1.15):

ρ(Eけ ;干PPPIhhI口~I

乞6引(Eιp、一寸Ekド - ReE(Ep))

k

乞8(Ep- Ek)

ρ。(Ep).

( 4.20)

(4.21)

Therefore， according to our calculation， the disappearance of the sharp DOS peak at

Ep reported above is not due to intrinsic phenornena but due to the limited resolution，


ー0.1nu nu

v

ltjh・日-Y1・4

e

」

Uy

一41nuu

一OMM

一

nH

一E」

一

円

uv

一

nH

一nJ』AU。-mRU

λ= 2.6 ωE=100meV

ー-with electron-phonon coupling

. without electron-phonon coupling original DOS

0.3

(ωtcコ.0」伺)と一ωcω吉一

= 100 meV [4.6]，

2W = 100 meV and the instrumental resolution 30 meV， corresponding to the high-

The dashed and solid lines are the

2.6，ωE 入Calculation with realistic parameters. Figure 4.5:

resolution measurement for the Ni borcトcarbides.

result with and without the electron-phonon interaction， respectively.

However， our which means that we could observe it clearly with higher resolution.

experimental spectra seem to show no signs of such a peak at Ep as shown in Fig. 2.16.

Then to explain this disappearance of the peak through the electron-phonon interaction，

the k-dependence of the self-energy may have to be taken into account. Nevertheless

this model calculation can explain to some extent the spectral weight transfer to the

higher binding energies for the Ni borか carbidesand the Chevrel-phase compounds.

For the Chevrel-phase compounds， however， the discrepancies between the experiments

and the band-structure calculations occurs away from Ep as well and its energy scale

is much larger than the typical phonon energies in this material， which means that

the discrepancies away from E F could not be explained only by this model even if the

electron-phonon interaction makes a significant influence on the photoemission spectra.


4.4 Conclusion

We have performed simple calculations including electron-phonon interaction based on

Engelsberg&Schrieffer's theory to clarify the cause of the discrepancies between the

experiments and the band-structure calculations for the boro-carbides and the Chevrel-

phase compounds. The electron-phonon interaction changes the photoemission spectra

significantly resulting in the spectral weight transfer to higher binding energies. It

is supposed that the k-dependence of the self-energy must be considered to explain

the significant suppression of the sharp DOS peak at Ep as observed in YNi2B2C.

At the same time， only the electron-phonon interaction is insu伍cientto explain the

discrepancies in the spectra of the Chevrel-phase compounds.

References

[4.1] M. Knupfer， M. Merkel， M. S. Golden， J. Fink， O. Gunaarsson and V. P.

Antropov， Phys. Rev. B 47， 13945 (1993).

[4司 S.Engelsberg and J. R. Schrieffer， Phys. Rev. 131， 993 (1963).

[4司 W~ L. McMillan， Phys. Rev. 167， 331 (1968).

[4.4] N. Tsuda， K. N錨 u，A. Fujimori and K. Siratori， Electronic Conduction in Oxides

2nd edition， (Shokabo， Tokyo， 1993)， Chap.2， in Japanese.

[4.5] C. Kittel， Quantum theory 01 solids， (Wiley， 1963).

[4.6] W. E. Pickett and D. J. Singh， Phys. Rev. Lett. 72， 3702 (1994).

101

102 REFERENCES

7¥

Appendix A

Engelsberg&Schrieffer's Theory

Here we briesy deduce Eqs. (4.11) and (4.12) according to Engelsberg and Schrief・

fer [4.斗

The electron self-energy E(P) can be expressed in the following diagram (Fig. A.l).

Here， r is the vertex part， G is the electron Green's function， and D is the phonon

E(p，ω1) = G(k，ε)

Figure A.1: Diagram representing the electron self-energy.

Green'sfunction. We define the Fermi level at f = O.

Here， r may be replaced by a unity， which means that the vertex corrections are ne-

glected according to the Migdal's theorem. Furthermore， the electron Green's function

will be treated self-consistently， whereas the phonon Green's function will not. Then

each Green's function is given:

G(k， E) =ー 1- f~ - E(k， f

(A.1)

and

D(ム← 9PE (A.2) e-- 1凶 E- HJ

103

104 APPENDIX A. ENGELSBERG&SCHRIEFFER 'S THEORY

where Einstein model with the constant phonon frequency WE is assumed and the

electron have the dispe凶 onrelation f2. Then the diagram of the self-energy considered

here is expressed as shown in Fig. A.2: In these approximations， the self-energy can be

')=~γ~ Figure A.2: Diagram representing the electron self-energy in which the vertex correction

is neglected. D is not treated self-consistently， which is expressed by a single-wavy line.

expressed:

~(p， ω) g2f MK ーっD(p-k，ω-f)G(k， f) 円1

(A.3)

? r df d3k 2ωE 1 1，0- I 一一一一一一~ J (2π)4 (ω-f)2 -(ωE一切)2 f -E2 -~ (k， f)"

(A.4)

If we assume that the density of state (DOS) has electron-hole symmetry with constant

intensity (ρ。)and that the self-energy ~(k ， f) is independent of k， then the above is

simplified into

f∞バf r∞ 2ωE 1 ~(ω) = ig2ρo I :: I

よ∞ 2π よ∞ (ω-E)2 -(ωE一切)2f - e -~(ε)" (A.5)

In addition， by defining

f - ~(E) = EZ(ε)， (A.6)

where Z is an appropriate function dependent only on E， we obtain

f∞ dE r∞ 2ωE fZ(ε) ~(ω)= 切らo I ;~ I

よ∞ 2π よ∞ (ω-E)2 -(ωE -'/，η)2 ( (A.7)

Judging from the imaginary part of the E(ε)， the following holds because the Fer口rm

level is located at E = 0:

1m EZ(ε) > 0 for E> 0

1m fZ(ε) < 0 for正<0(A.8)

、

105

Using above relation， the integration in Eq.(A.7) can be perfonned to be reduced into

E(ω) = ーの山 II αε -I α) I '" 1 ¥J-∞-- Jo --} (ω-f)2 -(ωE-iη)2 (A.9)

_g2ρo ln Iω+ωE- 1，~) 1ω-ωE十 Zη/

(A.I0)

The real and imaginary part of Eq.(A.lO) can be easily obtained to yield using入=

2g2ρ0/ωE:

and

Re E(ω) = -~ÀwEln I己WEI.&. IWー ωEI

j=-jπ入ωEsgn(ω) for 1ω1>ωE ImE(ω) <ー

l = 0 for 1ω1<ωE

The above equations are just what we would like to obtain.

(A.ll)

(A.12)

106 APPENDIX A. ENGELSBERG&SCHRIEFFER'S THEORY

，

Acknowledgments

1 would like to thank Prof. A. Fujimori for having suggested this work and always

giving me instruction full of encouragement. 1 acknowledge Dr. T. Mizokawa for his

fruitful advice both on experiments and analysis.

1 acknowledge Prof. H. Takagi， Dr. H. Eisaki， Prof. S. Uchida， Dr. R. J. Cava，

Dr. J. J. Kraおwski，and Dr. W. F. Peck， Jr. for kindly providing me thesamples

of the boro四carbidestogether with technical suggestion. 1 would like to thank Dr. L.

F. Mattheiss for kindly presenting me the resu1ts of the band-structure calculations

including unpublished results. 1 acknowledge Prof. S. Shin and Dr. A. Agui for

introducing me the soft x-ray emission spectroscopy for the boro-carbides and for giving

me fruitful discussion at the same time.

1 wish to thank Prof. T. Ohtani for providing me the samples of the Chevrel-phase

compounds. He also gave me kind advice and checked part of this thesis.

Through more than two years that 1 spent in Fujimori Laboratory， 1 greatly owe

the following people: Prof. D. D. Sarma， Prof. H. Namatame， Dr. A. E. Bocquet，

Dr. O. Radar， Dr. M. Nakamura， Dr. K. Morikawa， Dr. K. Shimada， Dr. T. Saitoh，

Mr. K. Mamiya， Mr. A. Sekiyama， Mr. K. FUjioka， Mr. T. Konishi， Mr. J. Y. Son，

Mr. A. Ino， Mr. T. Susaki， Mr. J. Okamoto， Mr. T. Tsujioka， Mr. J. Matsuno， Mr.

K. Ohotomo and Ms. H. Wakazono・Amongthem， 1 would like to express my special

appreciation to Mr. A. Sekiyama and Mr. K. Mamiya. Mr. A. Sekiyama has taught me

all about experiments and always gives me useful advice. Mr. Mamiya kindly helped

me installing 1虹EXand other necessaries， which greatly promoted this thesis.

Part of the calculations in the present thesis were performed by the VAX/VMS

in Faculty of Science， University of Tokyo. 1 also thank the staff of the Synchrotron

Radiation Laboratory for technical support. The present work is supported by a Grant-

in-Aid for Scientific Research from the Ministry of Education， Science and Culture.

Last but not le錨 t，1 thank my parents， brother and sister.

107

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Photoemission study of intermetallic superconductors: Boro ...wyvern.phys.s.u-tokyo.ac.jp/f/Research/arch/MasterThesis_K Kobayashi.pdf · Chapter 1 Introduction 1.1 Compounds Studied