Adam Kaminski Ames Laboratory and Iowa State University

High temperature superconductivity - insights from Angle Resolved Photoemission Spectroscopy

Funding:Ames Laboratory - US Department of Energy

Ames Laboratory Spectroscopy Group:

Takeshi Kondo - postdoctoral researcherAri Palczewski - Ph. D. studentJames Koll - undergraduate assistant

Collaborators:

Jörg Schmalian - ISURustem Khassanov - University of Zürich, SwitzerlandJanusz Karpinski - ETH, SwitzerlandJoel Mesot - PSI, SwitzerlandTakafumi Sato - Tohoku University, JapanTakashi Takahashi - Tohoku University, JapanHelene Raffy - Universite Paris-Sud, FranceKazuo Kadowaki - University of Tsukuba, Japan

Outline:

- condensed matter physics - is there anything left to understand?

- properties of conventional and “high temperature” superconductors

- introduction to Angle Resolved Photoemission Spectroscopy

- electronic properties of high temperature superconductors

- new results

condensed matter physics - is there anything left to understand?

all physics covered by electrodynamics + quantum mechanics

fortunately electrons in copper are weakly interacting and can be described by Landau Fermi Liquid model (1:1 correspondence with free electron gas), but in many systems the interactions are strong and current state of the art calculations can deal with ... 7x7 lattice

US penny: 3.1 grams of copper, 2.9x1022 electrons

a DVD has 4x1010 bitsso to store information only about spin for each electron we

need: 7.25 x 1011 DVD’s, but this is clearly not enough to do any meaningful calculations

... but complexity and new phenomena arise from large numbers of interacting particles

SuperconductivityDiscovered in 1911 by Kamerlinght Onnes first in mercury, then many other metals and alloys

resi

stan

ce [O

hm]

temperature [K]

Complete theory (BCS) due to Bardeen, Cooper and Schrieffer in 1957

Superconductivity

pairing + condensation

pair of two electron is a boson

bosons can condense creating

superfluid

In the metals electrical resitance arises due to scattering of the conduction

electrons from defects

E

In BCS the attractive pairing interaction between electrons arises from interaction

with the lattice vibrations (phonons)

In the superconducting state current is being carried by superfluid - condensate of very large

number of electron pairs

AFM

T

carrier concentration

SC

T*

pseudogap

TN

metal

~ 0.15

Tc

High temperature superconductorsDiscovered in 1986 by Bednorz and Müller.

Observed so far only in materials that contain copper oxide.

Superconducting transition temperature (Tc) up to 130K.

BiO

BiO

BiO

BiO

SrOCuOCaCuOSrO

SrOCuOCaCuOSrO

BiO

3.17Å

b

a

c

unit cell

Bi2Sr2CaCu2O 8+x

Pairing mechanism - unknown

θ

z

a or bφ

detector

analyzer

ARPES experiment

sample

High resolution UV beamline at Synchrotron Radiation Center, Wisconsin

undulator

hv

e-800 MeV ring at

Synchrotron Radiation Center

electron analyzer

sample

grating

samplelens

hemisphericalanalyzer

detector2D

photoelectrons

Electron analyzer

... high precision lab-based ARPES system

Energy resolution:~1.2 meV

Angular resolution:0.1 deg.

UV source:1013 photons/sec.

From atoms to solids:

two isolated atoms

two atom molecule

solid

Kittel - “Solid state physics”

Dispersion relation - energy bands

insulator

metal

Kittel - “Solid state physics”

θ

z

a or bφ

detector

analyzer

ARPES experiment

We need:binding energy - Eb initial momentum - ki

sampleEb = E - hv + W

ki||=kf

|| = √2mE/h2 sinθ

ki|=0 for quasi 2D samples

Nor

mal

ized

inte

nsity

-400 -300 -200 -100 0Energy [eV]

typical photoemission spectrum from Bi2212Bi 4f5/2 & 4f7/2

Nor

mal

ized

inte

nsity

-140 -138 -136 -134 -132 -130 -128

Energy [eV]

T=300K T=40K

Sr3d3/2,Sr3d5/2Theta=5 deg, hv=500 eV

Bi 5f1/2 , 5f3/2

Nor

mal

ized

inte

nsity

-355 -350 -345 -340Energy [eV]

Emission angle:

0 deg 10 deg 20 deg 30 deg 40 deg 50 deg

Ca2p1/2, Ca2p3/2hv=500 eV

Nor

mal

ized

inte

nsity

-285 -280 -275 -270 -265 -260

Energy [eV]

Sr3p1/2,Sr3p3/2Theta=5 deg, hv=500 eV

C 1s

T=300K T=40K

valence band

conduction band

150x103

100

50

0

Inte

nsity

[co

unts

/5m

in]

-8 -6 -4 -2 0Energy [eV]

Valence and conduction bands - simplest example: poly Au

Nor

mal

ized

inte

nsity

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2Energy [eV]

T=100KT=350K

Au 5d

valence band

conduction band

Eb(k1)"Ef"

hν

E

Ef

W

Electronic structure

k1 kk2

Evac

kf

ARPES spectra

hν

Typical “modern” ARPES data:

ARP

ES In

tens

ity

0.5 0.4 0.3

k (A-1)

E=const Momentum Distribution Curve (MDC)

ARP

ES In

tens

ity-0.3 -0.2 -0.1 0.0

Energy [eV]

k=const Energy Distribution Curve (EDC)

kE

I=<Ψi|A●p|Ψf>2A(k,ω) f(ω)symmetry of Ψ electronic structure

and interactionsA. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)

-0.6 -0.4 -0.2 0.0 0.2Energy [meV]

-0.6 -0.5 -0.4 -0.3

ky [A-1]

EDC MDCIntensity plot

-0.5

-0.4

-0.3

-0.2

-0.1

0.0

0.1

Ener

gy [

eV]

momentum

Eli Rotenberg, Advanced Light Source

C. G. Olson, D. W. Lynch et al.,Science 245, 731-733 (1989)

Superconducting gap

E

kµ

kf

T>TcT<Tc

2 !

J. C. Campuzano et al., Phys. Rev. B 53, 14737 (1996)

d-wave order parameter

H. Ding et al., Phys. Rev. B 54, 9678 (1996)

-1

0

1

10-1kx [π/a]

(0,0) (π,0)Fermi surface M

M

M

YX

XY

node anti-node

Nor

mal

ized

inte

nsity

-100 -80 -60 -40 -20 0 20 40

Energy [meV]

Superconducting stateLuNi2B2C (Tc=16K)T=9.5K

-15 -10 -5 0 5 10

Energy [meV]

5.0 meV

Laboratory system: Scienta analyzer and He Lamp

S. Souma et al., Nature, 423, 65 (2003)

Text

Collective modes

k,ω

k-q,ω-Ω

e

e

q,Ω

Interaction of electrons with a phonon:

Ashcroft and Mermin “Solid State Physics”

Renormalization effects along nodal direction

T. Valla et al., Science 24, 2110 (1999) P.V. Bogdanov et al., Phys. Rev. Lett. 85, 2581 (2001)A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)

k

-0.20

-0.15

-0.10

-0.05

0.00

Interaction of the electrons with a collective mode

T=40KT=140K

Node

AntinodeΓ Μ

Μ

NA

Mode energy

Based on the dispersion we can conclude that the interaction with the collective mode occurs only in the superconducting state, its energy is constant throughout the Brillouin zone and its strength increases significantly towards the antinode. These properties are consistent with the resonant mode observed by Inelastic Neutron Scattering (INS) experiments.

2.0

1.5

1.0

0.5

0.0

v F [e

V A

ng]

1.00.90.80.70.60.5kx [π/a]

Fermi velocity in the normal state

dispersion in normal and superconducting state

40

30

20

10

0

Vh/V

l

1.00.90.80.70.60.5

kx(π/a)

strength of coupling in the SC state

-1

0

1

10-1kx [π/a]

A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)

-0.3 -0.2 -0.1 0.0

k=(1,0)

k=(1,.365) -0.3 -0.2 -0.1 0.0

k=(.730,0)

k=(.730,.365) -0.3 -0.2 -0.1 0.0

k=(.640,0)

k=(.640,.365) -0.3 -0.2 -0.1 0.0

k=(.550,0)

k=(.550,.365) -0.3 -0.2 -0.1 0.0k=(.450,.365)

k=(.450,0)

-0.3 -0.2 -0.1 0.0

k=(.590,0)

k=(.590,.365)

Binding Energy (eV)

EDC’s in the superconducting state

NodeAntinode

A. Kaminski et al., Phys. Rev. Lett. 86, 1070 (2001)

Properties of the bosonic mode compatibility magnetic phonons

1) isotropic energy ∆+Ω yes yes

2) momentum anisotropy yes yes, recently

3) temperature dependence yes not obvious

4) doping dependence yes not obvious

Collective mode “score” card

Ag on Ag(111)Cu on Cu(111)

Scattering in traditional STM

SPECS website

Autocorrelated (AC) ARPES - new tool in studies of scattering processes

-12 meV

AC ARPES: q-space

Fourier transform

FT STM

J. E. Hoffman et al, Science 295, 466 (2002)

J. E. Hoffman et al, Science 297, 1148 (2002)

K. McElroy et al, Nature 422, 592 (2004)

L. Capriotti et al, PRB 68, 014508 (2003)

R. S. Markiewicz et al, PRB 69, 214517 (2004)

1.0

0.5

0.0

-0.5

-1.0

k x [π /

a]

1.00.50.0-0.5-1.0

kx [π/a]

-12 meV

ARPES intensity map

ARPES data and q-spaceq-space map

1.0

0.5

0.0

-0.5

-1.0

q x [π /

a]

1.00.50.0-0.5-1.0qx [π/a]

q1q2

q3

q4

q6q5

q7

q1q2

q3

q4

q6q5

q7

S(q,!= !0) = "kx,ky

I(k,!) I(k+q,!)

AutoCorrelated (AC) ARPES -

-12 meV

ARPES intensity maps

-12 meV

AC ARPES: q-space

q-space

Comparison of FT STM and AC ARPES

q1

q3

q1

q3

K. McElroy et al, Nature 422, 592 (2004)

U. Chatterjee et al, Phys. Rev. Lett. (submitted)

Conclusions:

- ARPES is an excellent probe to study electronic properties of strongly correlated systems such as heavy fermion systems and high temperature superconductors

- the only relevant feature in electronic structure for high temperature superconductivity is a hole pocket Fermi surface centered at kx=ky=1

- bridging the results from ARPES and FT STM will lead to better understanding of low energy excitations and possibly high temperature superconductivity