Universal Features of the Mott-Metal Crossover in the Hole Doped …qcmjc/talk_slides/QCMJC.2014.08.28_Umesh.pdf · 28-08-2014 · doped Mott-insulators across the Mott-metal crossover

Universal Features of the Mott-Metal Crossover inthe Hole Doped J = 1/2 Insulator Sr2IrO4

Umesh Kumar Yadav

Centre for Condensed Matter TheoryDepartment of Physics

Indian Institute of Science

August 28, 2014

Quantum Condensed Matter Journal Club

Umesh Kumar Yadav (Centre for Condensed Matter Theory Department of Physics Indian Institute of Science)Universal Features of the Mott-Metal Crossover in the Hole Doped J = 1/2 Insulator Sr2IrO4August 28, 2014 1 / 27

Outline of the talk

What are the Mott-Hubbard, Charge Transfer and Slater Insulators ?

What are the J = 1/2 Insulators ?

How do Iridates differ from Cuprates ?

What are the common features of doped Iridates and Cuprates ?

What are the causes of universal features of Mott-metal crossover inthe Iridates ?

Is Sr2IrO4 Mott insulator or Slater insulator ?

Conclusions and future directions


Let us start the talk with followings

The physics of the doped Mott-insulators is controversial since a longtime.

Problem to understand their physics are followings:

1. Strong electron correlations,2. Competing electronic orders e.g. in case of cuprates charge densitywave and stripe order,3. Long range magnetic order,4. Fluctuations and Fermi surface instabilities,5. etc . . .

Common understanding:

Charge insulation in most known Mott insulators arises due to“Coulomb repulsion” only.


As an example consider the case of hole doped Cuprates

Understanding the origin of exotic phases like Pseudogap and Strangemetal (Marginal Fermi liquid) is not clear.

There are many proposals that they arise because of:

1. Metal-insulator transition,2. Some density wave instabilities,3. Fluctuations of the superconductivity,4. Existence of a Quantum critical point,5. etc . . .

Are really they responsible ?


Can we do something simple ?

One can ignore it.

But as we know after finding the conventional SC (Liquid He, 1911)it took around 46 years to have a microscopic theory known as “BCStheory” (1957).

Cuprates are only 28 years old (first Cuprate, La2−xBaxCuO4, wasdiscovered in 1986), we still have some hope.

We could try a system with clean phase diagram (Hence Lessercompeting orders) and different mechanism which forbids electrondouble occupancy.

One example of such systems is Rh doped Sr2IrO4.

Goal: To find the universal features (Low energy properties that donot depend on the details of the interactions) and their origin fordoped Mott-insulators across the Mott-metal crossover.


Mott-Hubbard and charge transfer insulators1.1. Strongly correlated system 9

Figure 1.1.2 (a) Schematic band structure of a Mott Hubbard insulator. The p-band lies before the d-band, and the low energy charge excitations occur between the lower and upper Hubbard band. (b) Schematic band structure of a Charge-Transfer insulator. The p-band lies between the lower and upper Hubbard band. The lower energy charge excitation involves the d and p-bands.

Figure 1.1.3 Zaanen-Sawatzky Allen Δ−U diagram for (a) divalent and (b) higher valent

transition metal compounds study by ref. [26]. The regime above the line U=Δ is the charge

trasfer regime while the regime below this line is the Mott-Hubbard regime.

(a) Mott-Hubbard Insulator (b) Charge-Transfer Insulator

(a) (b)

εF

interaction U U

Charge gap

d-band

p-band

Δ=|εd-εp|

p-band

U

d-band

interaction U Δ=|εd-εp|

Fermi level,εF

charge gap


Slater insulators: Magnetically driven insulatorsSlater insulators

Weak coupling insulator due to LRO

a

2a

E(k)

−1/a 1/a k −1/2a 1/2a

EF

k

E(k)

soft – gap in SSB at T < Tc

spin – density wave (SDW)

〈Sz(x)〉 ∼ ∆ cos(2kFx)

E(k) = EF ±q

ε2k + ∆2, ∆(T ) ∼

√Tc − T

thermodynamic MITsUmesh Kumar Yadav (Centre for Condensed Matter Theory Department of Physics Indian Institute of Science)Universal Features of the Mott-Metal Crossover in the Hole Doped J = 1/2 Insulator Sr2IrO4August 28, 2014 7 / 27

Electronic structure of the elements of our interest

La2−xSrxCuO4:57La − [Xe] 5d16s2

38Sr − [Kr ] 5s2

29Cu − [Ar ] 3d104s1 → Cu2+ − 3d9

8O − 1s22s22p6

Sr2Ir1−xRhxO4:77Ir − [Xe] 4f 145d76s2 → Ir 4+ − 5d5

45Rh − [Kr ] 4d85s1 → Rh4+ − 4d5

Ir and Rh are isovalent.


Cuprates: Charge-transfer insulator

work by C. P. Slichter and early transport measurementsby N. P. Ong among others. Discussions of stripe physicswere recently given by Carlson et al. �2003� and Kivelsonet al. �2003�. A discussion of spin-liquid states is given bySachdev �2003�, with an emphasis on dimer order and byWen �2004�, with an emphasis on quantum order. For anaccount of experiments and early RVB theory, see thebook by Anderson �1997�.

II. BASIC ELECTRONIC STRUCTURE OF THE CUPRATES

It is generally agreed that the physics of high-Tc su-perconductivity is that of the copper-oxygen layer, asshown in Fig. 2. In the parent compound such asLa2CuO4, the formal valence of Cu is 2+, which meansthat its electronic state is in the d9 configuration. Thecopper is surrounded by six oxygens in an octahedralenvironment �the apical oxygen lying above and belowCu are not shown in Fig. 2�. The distortion from a per-fect octahedron due to the shift of the apical oxygenssplits the eg orbitals so that the highest partially occu-pied d orbital is x2−y2. The lobes of this orbital pointdirectly to the p orbital of the neighboring oxygen, form-ing a strong covalent bond with a large hopping integraltpd. As we shall see, the strength of this covalent bondingis responsible for the unusually high energy scale for theexchange interaction. Thus the electronic state of thecuprates can be described by the so-called three-bandmodel, where in each unit cell we have the Cu dx2−y2

orbital and two oxygen p orbitals �Emery, 1987; Varmaet al., 1987�. The Cu orbital is singly occupied while the porbitals are doubly occupied, but these are admixed by

tpd. In addition, admixtures between the oxygen orbitalsmay be included. These tight-binding parameters maybe obtained by fits to band-structure calculations �Mat-theiss, 1987; Yu et al., 1987�. However, the largest energyin the problem is the correlation energy for doubly oc-cupying the copper orbital. To describe these correlationenergies, it is more convenient to refer to the hole pic-ture. The Cu d9 configuration is represented by energylevel Ed occupied by a single hole with S= 1

2 . The oxygenp orbital is empty of holes and lies at energy Ep, which ishigher than Ed. The energy to doubly occupy Ed �lead-ing to a d8 configuration� is Ud, which is very large andcan be considered infinity. The lowest-energy excitationis the charge-transfer excitation in which the hole hopsfrom d to p with amplitude −tpd. If Ep−Ed is sufficientlylarge compared with tpd, the hole will form a local mo-ment on Cu. This is referred to as a charge-transfer in-sulator in the scheme of Zaanen et al. �1985�. Essentially,Ep−Ed plays the role of the Hubbard U in the one-bandmodel of the Mott insulator. Experimentally an energygap of 2.0 eV is observed and interpreted as the charge-transfer excitation �see Kastner et al., 1998�.

Just as in the one-band Mott-Hubbard insulator inwhich virtual hopping to doubly occupied states leads toan exchange interaction JS1 ·S2, where J=4t2 /U, in thecharge-transfer insulator the local moments on nearest-neighbor Cu prefer antiferromagnetic alignment be-cause both spins can virtually hop to the Ep orbital. Ig-noring the Up for doubly occupying the p orbital withholes, the exchange integral is given by

J =tpd4

�Ep − Ed�3 . �1�

The relatively small size of the charge-transfer gapmeans that we are not deep in the insulating phase andthe exchange term is expected to be large. Indeed ex-perimentally the insulator is found to be in an antiferro-magnetic ground state. By fitting Raman scattering totwo magnon excitations �Sulewsky et al., 1990�, the ex-change energy is found to be J=0.13 eV. This is one ofthe largest exchange energies known. �It is even larger inthe ladder compounds which involve the same Cu-Obonding.� This value of J is confirmed by fitting the spin-wave energy to theory, in which an additional ring ex-change term is found �Coldea et al., 2001�.

By substituting divalent Sr for trivalent La, the elec-tron count on the Cu-O layer can be changed in a pro-cess called doping. For example, in La2−xSrxCuO4, xholes per Cu are added to the layer. As seen in Fig. 2,due to the large Ud the hole will reside on the oxygen porbital. The hole can hop via tpd, and due to transla-tional symmetry the holes are mobile and form a metal,unless localization due to disorder or some other phasetransition intervenes. The full description of hole hop-ping in the three-band model is complicated, and a num-ber of theories consider this essential to the understand-ing of high-Tc superconductivity �Emery, 1987; Varma etal., 1987�. On the other hand, there is strong evidencethat the low-energy physics �on a scale small compared

FIG. 2. �Color online� Electronic structure of the cuprates. �a�Two-dimensional copper-oxygen layer �left� simplified to theone-band model �right�. �b� The copper d and oxygen p orbit-als in the hole picture. A single hole with S=1/2 occupies thecopper d orbital in the insulator.

21Lee, Nagaosa, and Wen: Doping a Mott insulator: Physics of high-¼

Rev. Mod. Phys., Vol. 78, No. 1, January 2006


Sr2IrO4: Spin-Orbit coupled J = 1/2 Mott-insulator

�ð!Þ was obtained by using Kramers-Kronig (KK) trans-formation. The validity of KK analysis was checked byindependent ellipsometry measurements between 0.6 and6.4 eV. XAS spectra were obtained at 80 K under vacuumof 5� 10�10 Torr at the Beamline 2A of the Pohang LightSource with �h� ¼ 0:1 eV.

Here we propose a schematic model for emergence of anovel Mott ground state by a large SO coupling energy �SOas shown in Fig. 1. Under the Oh symmetry the 5d statesare split into t2g and eg orbital states by the crystal field

energy 10Dq. In general, 4d and 5d TMOs have suffi-ciently large 10Dq to yield a t52g low-spin state for

Sr2IrO4, and thus the system would become a metal withpartially filled wide t2g band [Fig. 1(a)]. An unrealistically

large U � W could lead to a typical spin S ¼ 1=2 Mottinsulator [Fig. 1(b)]. However, a reasonable U cannot leadto an insulating state as seen from the fact that Sr2RhO4

is a normal metal. As the SO coupling is taken intoaccount, the t2g states effectively correspond to the orbital

angular momentum L ¼ 1 states with ml¼�1 ¼ �ðjzxi �ijyziÞ= ffiffiffi

2p

and ml¼0 ¼ jxyi. In the strong SO coupling

limit, the t2g band splits into effective total angular mo-

mentum Jeff ¼ 1=2 doublet and Jeff ¼ 3=2 quartet bands[Fig. 1(c)] [17]. Note that the Jeff ¼ 1=2 is energeticallyhigher than the Jeff ¼ 3=2, seemingly against the Hund’srule, since the Jeff ¼ 1=2 is branched off from the J5=2(5d5=2) manifold due to the large crystal field as depicted in

Fig. 1(e). As a result, with the filled Jeff ¼ 3=2 band and

one remaining electron in the Jeff ¼ 1=2 band, the systemis effectively reduced to a half-filled Jeff ¼ 1=2 single bandsystem [Fig. 1(c)]. The Jeff ¼ 1=2 spin-orbit integratedstates form a narrow band so that even small U opens aMott gap, making it a Jeff ¼ 1=2Mott insulator [Fig. 1(d)].The narrow band width is due to reduced hopping elementsof the Jeff ¼ 1=2 states with isotropic orbital and mixedspin characters. The formation of the Jeff bands due to thelarge �SO explains why Sr2IrO4 (�SO � 0:4 eV) is insulat-ing while Sr2RhO4 (�SO � 0:15 eV) is metallic.The Jeff band formation is well justified in the LDA and

LDAþU calculations on Sr2IrO4 with and without in-cluding the SO coupling presented in Fig. 2. The LDAresult [Fig. 2(a)] yields a metal with a wide t2g band as in

Fig. 1(a), and the Fermi surface (FS) is nearly identical tothat of Sr2RhO4 [12,13]. The FS, composed of one-dimensional yz and zx bands, is represented by holelike� and �X sheets and an electronlike �M sheet centered at�, X, and M points, respectively [12]. As the SO couplingis included [Fig. 2(b)], the FS becomes rounded but retainsthe overall topology. Despite small variations in the FStopology, the band structure changes remarkably: Twonarrow bands crossing EF are split off from the rest due

FIG. 1. Schematic energy diagrams for the 5d5 (t52g) configu-ration (a) without SO and U, (b) with an unrealistically large Ubut no SO, (c) with SO but no U, and (d) with SO and U.Possible optical transitions A and B are indicated by arrows.(e) 5d level splittings by the crystal field and SO coupling.

E-EF (eV)

M X

E-EF (eV)

M X

Γ

M

X

E-µ (eV)

M X

(a) LDA

M

M

Γ

Γ

X

X

Γ

M

X

E-EF (eV)

M X

Γ

Γ

Γ

Γ Γ

Γ

Γ

Γ

αβM

βX

α βX

(b) LDA+SO

(c) LDA+SO+U

(d) LDA+U

FIG. 2 (color online). Theoretical Fermi surfaces and banddispersions in (a) LDA, (b) LDAþ SO, (c) LDAþ SOþU(2 eV), and (d) LDAþU. In (c), the left panel shows topologyof valence band maxima (EB ¼ 0:2 eV) instead of the FS.

PRL 101, 076402 (2008) P HY S I CA L R EV I EW LE T T E R Sweek ending

15 AUGUST 2008

076402-2


Phase diagram of La2−xSrxCuO4 (LSCO) cuprate

26 CHAPTER 4. OVERVIEW OF LSCO

4.3 The LSCO phase diagram

To which extent the crystal shows IC static order, IC fluctuations or both depends on the dopingvalue and the temperature. The phase diagram shows the magnetic transition temperature(TN ) and superconducting transition temperature (Tc) as a function of doping and divide thecrystals into different phase regimes. These phase regimes are not fully understood, but thereare some general features, which allow for a division into different regimes. The phase diagramhas been drawn in Fig. 4.4.

Figure 4.4: Phase diagram of La2−xSrxCO4 (LSCO).

For dopings below 0.05 the crystal is an antiferromagnetic Mott insulator drawn as thered area in Fig. 4.4. Above this doping value superconductivity (SC) sets in and for dopings0.05 < x < 0.13 static IC magnetism, the so-called spin-density wave (SDW), is also present.The groundstate is thus some kind of combined state, where static IC order co-exists withsuperconductivity. Above the doping value of x = 0.13 the elastic IC signal disappears, but ICfluctuations persist for higher doping. The doping value x = 0.16 is denoted optimal, since atthis doping value the transition temperature is maximal, Tc = 38 K.

For sufficiently high dopings superconductivity breaks down and the system becomes a nor-mal Fermi liquid. Whereas no explanation exists for the superconductivity in the underdopedregime the superconducting phase for high dopings is well described by BCS theory, becauseof its proximity to the Fermi liquid phase.

The exotic phase denoted the ”pseudogap”-phase refers to the observation that there is agap in the static spin susceptibility. Furthermore there is a suppression of the electronic densityof states at (kx, ky) = (π, 0). One interpretation of the pseudogap is that electrons combine intoso-called preformed pairs. The formation of pairs, i.e. spin singlets, causes the susceptibilityto decrease. The ”strange metal” phase has got its name due to a strange in-plane resistivity.The resistivity scales linearly with temperature instead of quadratically as does a normal Fermiliquid.

M.-H. Julien has collected magnetic resonance data on LSCO [15] and thereby constructeda LSCO phase diagram which include the transition temperature for the static IC order. His


An early stage Phase diagram of Sr2Ir1−xRhxO4

19

Fig.5


Details about samples used

All the ARPES, transport and magnetization data are taken from bulkSr2Ir1−xRhxO4 samples.

Self flux technique is used to grow single crystals from quantitiesSrCl2, SrCO3, IrO2 and RhO2.


Crystal Structure, MDC and schematic of energy bands

X

Figure 1

a c1

c2 J1/2 LHB J1/2 UHB E

Mott

J3/2

J1/2 LHB J1/2 UHB E

Mott

J3/2

µ!

EF

!" (#, 0)!

X/Y!

La2CuO4 Sr2IrO4

c3 (inconsistent with ARPES)

J1/2 LHB J1/2 UHB E

Mott

J3/2

µ!

b

!"

EB=0.2eV

(#, 0)!

!’"M

X


Resistivity and magnetism as a function of doping

Figure S1

Figure S1. The evolution of resistivity and magnetism with Rh doping. The left axis: the normalized resistivity; and the right axis the onset of the long-range magnetic order.

100101102103104105106

0.200.150.100.050.00

250

200

150

100

50

0

TN (K

) !(

2K)

/ ! (3

00K

)

Rh Doping


Band structure along high symmetry directions

Figure S2

Figure S2. The band structure along high symmetry directions in the parent and Rh doped Sr2IrO4. a. The Fermi surface topology of the x=15% Rh-doped sample. The high symmetry cuts in panels b to d are drawn in dashed orange line. b-d. The EDC second-derivative maps for the parent (b1-d1) and x=15% Rh-doped sample (b2-d2) respectively. The dashed lines are guides to the eye where the green and red colors denote the J=1/2 lower Hubbard band and J=3/2 band.

Sr2Ir0.85Rh0.15O4

EF

b

c

d

!" X

X !’

M

a

-1.2

-0.8

-0.4

0.0

-1.2

-0.8

-0.4

0.0

!"X X X !’ !’" X M X

Sr 2

IrO

4

E-E

F (

eV

) S

r 2Ir

0.8

5R

h0

.15O

4

E-E

F (

eV

)

b1 c1 d1

b2 c2 d2


MDC and ARPES EMIP at zero and finite dopings

Figure 2

a

b

c x=0% x=15%

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

E-E

F (

eV

)

(!, 0) "’# "’# (!, 0) "’# "’#

x=

0%

x=

15

%

200meV

400meV

EF

"#

"’#

(!, 0)

"#

"’#

(!, 0)

200meV

T = 50K


Understanding the process of hole doping

a b

2!SO/3

J=3/2

J=1/2

!SO/3

Ir4+ Rh4+

2!SO/3

J=3/2

J=1/2

!SO/3

Ir5+ Rh3+

Initial

Final

0.30

0.20

0.10

0.000.200.150.100.050.00

Rh Doping

"µ

(eV

)

Figure 3


Doping and temperature dependence of the gap

Figure 4

-0.20 -0.10 0.00 0.10

Rh=4% TN=170K

!1

Inten

sity (a

.u.)

E-EF (eV)

40

30

20

10

0

0.150.100.050.00

!1 !2

Gap S

ize (m

eV)

Rh Doping

a b

-0.20 -0.10 0.00 0.10E-EF (eV)

!2

Rh=15% TN=17K Int

ensity

(a.u.

)

c

e

d

-0.20 -0.10 0.00 0.10

FS1 FS2 25K 25K 50K 50K 75K 75K

Inten

sity (a

.u.)

E-EF (eV)

Rh=11% TN=57K

FS1

FS2 "#

"’#

Rh = 15%, T = 50K NFL

Ultra UDC

PG 6= LRAFM


Fitting of the EDC curves

The energy distribution curves (EDCs) are fitted with followingequation

BG + A+Bω1+e(ω+∆)/kBT∗

which is a Fermi function with variable edge width kBT ∗ and withleading edge midpoint shifted from the chemical potential by the gapvalue ∆. ω is the energy relative to Fermi energy and BG is thebackground counts. A and B are the fitting coefficients.


Resistivity as a function of temperature

Figure 5

a b c

-0.25

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

E-E F (

eV)

(-!, 0) (!, 0) "#

x=11%, T=50K 0.30

0.25

0.20

0.15

!"#$

%&'()*

-0.20 -0.15 -0.10 -0.05 0.00+,!!%&-.*

x=11%, T=50K

0 100 200 300 T (K)

0.025

0.020

0.015

0.010

x=11%

! a ($

cm)

FS1

FS2

"’#"#

O


Is Iridates or Slater insulator (SI) or Mott insulator (MI) ?

The SI is a mean field concept that ignores short range AFcorrelations.

At best one considers them as fluctuations of long range AF order.

One should expect that gap in SI would go zero as long range AFMorder tends to zero (around PT point).

As there is no clear change in band structure seen for parent anddoped compounds across the onset of long range AFM order.

It suggests that the long range magnetic order is not necessary tohave a gap in Iridates.

Sr2IrO4 is a “Mott insulator”.


Distortion in crystal structure and schematic of energybands

14

Fig. 1


Temperature dependence of resistivity

15

Fig. 2

10-9

10-1

101

103

105

0 50 100 150 200 250 300 350 400

log (

cm

)

c

a

(a)

Sr2IrO

4-

I = 0.05 mA

= 0

0 100

4 10-2

8 10-2

1.2 10-1

1.6 10-1

0 50 100 150 200 250 300 350 400

(

cm)

T (K)

c

a

(b)

I = 0.05 mA

TMI

Ta

0

100

200

300

0 100 200 300 400 500 600

S c (V/

K)

T (K)

= 0 Sr2IrO

4-

(c)

2.5 10-2

3.5 10-2

0 100

2 10-4

4 10-4

6 10-4

0 5 10 15 20

c ( cm

)

a (cm)

T (K)

a ~ T

cT

a


Conclusions and future directions

A smooth crossover is seen from a “MI” Sr2IrO4 to a “bad metal”hole doped Sr2IrO4.

Doped Iridates exhibit all exotic features (means “Pseudogaps”,“Fermi arcs” and “MFL”) that are present in Cuprates, despite thedifferent mechanism that forbids electron double occupancy.

Universal features of Mott-metal crossover are not related topreformed electron pairing, quantum criticality or density waveinstabilities.

The “short range Anti-Ferromagnetic correlations” are playingindispensable role to govern the exotic properties of Iridates.

Sr2IrO4 is a “Mott insulator”.

The “short range AFM correlations” may be responsible for the“Pseudogaps” and “SM” phases in the Cuprates too.

Due to large “Spin-orbit coupling” in Sr2IrO4, it may be aninteresting “Topological insulator” system.


References

Yue Cao, Qiang Wang, Justin A. Waugh, Theodore J. Reber, Haoxiang Li,

Xiaoqing Zhou, Stephen Parham, Nicholas C. Plumb, Eli Rotenberg, Aaron

Bostwick, Jonathan D. Denlinger, Tongfei Qi, Michael A. Hermele, Gang

Cao and Daniel S. Dessau, arXiv:1406.4978, June 2014.

Jixia Dai, Eduardo Calleja, Gang Cao and Kyle McElroy, Phys. Rev B90, 041102(R) (2014).

T. F. Qi, O. B. Korneta, L. Li, K. Butrouna, V. S. Cao, XiangangWan, P. Schlottmann, R. K. Kaul, and G. Cao, Phys. Rev B 86,125105 (2012).

Fa Wang and T. Senthil, Phys. Rev Lett. 106, 136402 (2011).

O. B. Korneta, Tongfei Qi, S. Chikara, S. Parkin, L. E. De Long, P.Schlottmann and G. Cao, Phys. Rev B 82, 115117 (2010).


Thanks for your kind attention


Documents

Universal Features of the Mott-Metal Crossover in the Hole Doped …qcmjc/talk_slides/QCMJC.2014.08.28_Umesh.pdf · 28-08-2014 · doped Mott-insulators across the Mott-metal crossover