Predicting and Understanding Correlated Electron Materials: A Computational Approach

Rutgers Colloquium, 2008

Predicting and Understanding Correlated Electron Materials: A Computational Approach

Kristjan Haule

Collaborators: J.H. Shim & G. Kotliar

Outline

Standard theory of solids (Landau Fermi liquid, Density Functional Theory)

Complex correlated matter -> standard theory fails LDA+DMFT and its strengths Detailed comparison of LDA+DMFT results with experiment

s for a heavy fermion material CeIrIn5 Local Ce 4f - spectra and comparison to AIPES) Momentum resolved spectra and comparison to ARPES Optical conductivity and its connection to hybridization gaps Fermi surface in DMFT Sensitivity to substitution of transition metal ion: difference between

CeIrIn5, CeCoIn5 and CeRhIn5

References:•KH, J.H. Shim, and G. Kotliar, Phys. Rev. Lett 100, 226402 (2008)•J.H. Shim, KH, and G. Kotliar, Science 318, 1618 (2007).•J.H. Shim, KH, and G. Kotliar, Nature 446, 513 (2007).

Standard theory of solids-Standard theory of solids-

Fermi liquid theoryFermi liquid theory

Excitation spectrum of a fermion system has the same structure as the

excitation spectrum of a perfect Fermi gas.

Lev Davidovich Landau

One to one correspondence between the interacting system and Fermi gas

Nobel laureate 1962Rigid band

Well defined quasiparticles->Rigid bands with long lifetime

fundamentals

Becomes quantitative/predictiveBecomes quantitative/predictive

Kohn-Hohenberg-Sham (1964):One-to-one mapping between the interacting system in the ground state and Kohn-Sham system of non-interacting particles.

M

KL

Band Theory: electrons as waves: Rigid band picture: En(k) versus k

Walter Kohn,Nobel laureate 1998

All “complexity” hidden in the XC functional

Standard theory at workStandard theory at work

Very powerful quantitative tools were developed: Very powerful quantitative tools were developed:

DFT(LDA,LSDA,GGA) ,GWDFT(LDA,LSDA,GGA) ,GW

Predictions:

•total energies,

•stability of crystal phases

•optical transitions

M. Van SchilfgardeM. Van Schilfgarde

Complex electronic matterComplex electronic matter

Transition metal oxides

Oxygen

transition metal ion

Cage of 6 oxygen atoms (octahedra)

Build a microscopic crystal with this building block

Transition metal insideTransition metal ions

Rare earth ions

Actinides

Oxygen

V

Metal insulator transitionMetal insulator transition

Manning T. D. & Parkin I. P. J. Mater. Chem. ,14. Article (2004). Above 29º reflects heat,

Coating – smart window

V: Mott metal-insulator tr. at room TN. F. Mott, PRB 11, 4383 (1975)

VO2

Oxygen

Mn

Hard disk deviceGiant magnetoresistance

Albert Fert and Peter GrünbergNobel Laureate 2007

Mn: Colossal magnetoresistanceS.W. Cheong et.al., Nature 399, 560 (1999)

Colossal magnetoresistanceColossal magnetoresistance


LaMnO3+doping+layering

Oxygen

Co

Electronic refrigeration

Co: Giant thermopowerY. Wang et.al., Nature 423, 425 (2003)

Giant thermopowerGiant thermopower



NaxCo2O4

Oxygen

Ni,Ru

Electronic Electronic crystallization/nematiccrystallization/nematic

Ni: Electronic crystallizationJ. Tranquada et.al., PRL 73, 1003 (1993)



Ru: Electronic nematicR.A. Borzi et.al., Science 315, 214 (2007)


Electronic crystal

La2NiO4.125

Oxygen

Cu

Ni: Electronic crystallizationJ. Tranquada et.al., PRL 73, 1003 (1993)

High temperature High temperature superconductivitysuperconductivity



Ru: Electronic nematicR.A. Borzi et.al., Science 315, 214 (2007)

Cu: High temperature superconductorBednorz&Muller, Z Phys. 64, 189(1986) Nobel Laureate 1987


layering+doping

SmFxO1-xFeAs x~0.2 d)

Tc=55K, cm/0803.3603

a=3.933A, c=8.4287A

PrFxO1-xFeAs c) Tc=52K, cm/0803.4283

a=3.985A, c=8.595A

CeFxO1-xFeAs b) Tc=41 K, cm/0803.3790

a=3.996A, c=8.648A

LaFxO1-xFeAs a) Tc=26 K,

JACS-2008

a=4.036A, c=8.739 A

La1-xSrxOFeAs Tc=25K, cm/0803.3021,

a=4.035A, c = 8.771AS

maller

c,

perf

ect

an

gle

a) Hosono et.a.., Tokyo, JACSb) X.H. Chen, et.al., Beijing,arXiv: 0803.3790c) Zhi-An Ren, Beijing, arXiv: 0803.4283d) Zhi-An Ren, Beijing, arXiv: 0804.2053.

Fe high temperature Fe high temperature superconductorssuperconductors

Fe

As

Tetrahedral cage (rather than octahedral)

CeCoIn5 CeRhIn5 CeIrIn5 PuCoG5

Tc[K] SC 2.3K N 3.8 K SC 0.4K 18.3K

Tcrossover ~50K ~50K ~50K ~370K

Cv/T[mJ/molK^2] 300 400 750 100

CeCoIn5 CeRhIn5CeIrIn5 CeCoIn5

CeXIn5

Ce

InX

CeIn

In

Heavy fermion materials (115)Heavy fermion materials (115)

Ce atom in cage of 12 In atoms

Properties can be tuned (substitution,pressure, magnetic field) between

•antiferromagnetism•superconductivity•quantum critical point

AFM

SCSC

AFM+SC

•Need for new methods and techniques which can deal with strong electronic correlations

Strong correlation – Strong correlation –

Standard theory of solids failsStandard theory of solids fails

•The electronic matter in these materials has tremendous potential for applications (large response to small stimuli, variety of responses,…)

•But it involves strong electronic interactions and has proved

extremely difficult to understand

Fermi Liquid Theory does NOT work . Need new concepts to replace rigid bands picture!

Breakdown of the wave picture. Need to incorporate a real space perspective (Mott).

Non perturbative problem.

Coherent+incoherent spectra

Why does it fail?Why does it fail?

Rigid band

Bright future!Bright future!

New concepts, new techniques…..

1B HB model 1B HB model (DMFT):(DMFT):DMFT can describe Mott transition:

Dynamical Mean Field Theory the simplest approach which can describe the physics of strong correlations

->the spectral weight transfer->Mott transition->local moments and itinerant bands, heavy

quasiparticles

Weiss mean field theory for spin systemsExact in the limit of large z

Classical problem of spin ina magnetic field

Problem of a quantum impurity (atom in a fermionic band)

Space fluctuations are ignored, time fluctuations are treated exactly

DMFT in a Nutt shellDMFT in a Nutt shell

Dynamical mean field theory (DMFT) for the electronic problem

exact in the limit of large z

DMFT + electronic structure methodDMFT + electronic structure method

(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).

Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated orbitals (s,p): use LDA or GWFor correlated orbitals (f or d): add all local diagrams by solving QIM

DMFTmultiband&multiplets

OCA

SU

NC

A

NCALuttinger Ward functional

General impurity solvers: a diagrammatic real axis solver

Sum most important diagrams

General impurity problem

K.H., J Kroha & P. Woelfle, Phys. Rev. B 64, 155111 (2001)

General impurity problem

Diagrammatic expansion in terms of hybridization +Metropolis sampling over the diagrams

•Exact method: samples all diagrams!•Allows correct treatment of multiplets

K.H. Phys. Rev. B 75, 155113 (2007)

An exact impurity solver, continuous time QMC - expansion in terms of hybridization

K.H. Phys. Rev. B 75, 155113 (2007) ; P Werner, PRL (2007); N. Rubtsov PRB 72, 35122 (2005).

DMFT+LMTO package

http://www.physics.rutgers.edu/~haule/download.html

Database of materials

To be available at

Basic questions to addressBasic questions to address

How to compute spectroscopic quantities (single particle spectra, optical conductivity phonon dispersion…) from first principles?

How to relate various experiments into a unifying picture.

DMFT maybe simplest approach to meet this challenge for correlated materials

?

Issues in complex electronic matter

•Electronic properties are a strong function of temperature, pressure, doping

•Electronic states are developing in a nontrivial way in (,k) space (rigid band picture does not apply)

One example of a “heavy fermion” system, Ce-115’s:

•How does the crossover from localized moments to itinerant q.p. happen?

k

A()

•Where in momentum space q.p. appear and

how?

Crossover scale ~50K

in-plane

out of plane

•Low temperature – Itinerant heavy bands

•High temperature Ce-4f local moments

ALM in DMFTSchweitzer&Czycholl,1991

Coherence crossover in experiment

Temperature dependence of the local Ce-4f spectra

•At low T, very narrow q.p. peak (width ~3meV)

•SO coupling splits q.p.: +-0.28eV

•Redistribution of weight up to very high frequency

SO

•At 300K, only Hubbard bands

J. H. Shim, KH, and G. Kotliar Science 318, 1618 (2007).

CeIrIn5

A() – number of available states per energyA(k,) – number of available states

per momentum per energy ACe-4f()

Very slow crossover!

T*

Slow crossover pointed out by NPF 2004

Buildup of coherence in single impurity case

TK

cohere

nt

spect

ral

weig

ht

T scattering rate

coherence peak

Buildup of coherence

Crossover around 50K

Remarkable agreement with Y. Yang & D. Pines Phys. Rev. Lett. 100, 096404 (2008).

Anom

alo

us

Hall

coeffi

cient

Fraction of itinerant heavy fluid

m* of the heavy fluid

Consistency with the phenomenological approach of NPF

+const

ARPESFujimori, 2006

Angle integrated photoemission vs DMFT

Experiment at T=10K

Maybe surface sensitive at 122eV

Angle integrated photoemission vs DMFT

ARPESFujimori, Phys. Rev. B 73, 224517 (2006).

Nice agreement for the• Hubbard band position•SO split qp peak

Hard to see narrow resonance

in ARPES since very little weight

of q.p. is below Ef

Lower Hubbard band

T=10K T=300Kscattering rate~100meV

Fingerprint of spd’s due to hybridization

Not much weight

q.p. bandSO

Momentum resolved Ce-4f spectraAf(,k)

Hybridization gap

CeIn

In

Optical conductivity

Typical heavy fermion at low T:

Narrow Drude peak (narrow q.p. band)

Hybridization gap

k

Interband transitions across hybridization gap -> mid IR peak

CeCoIn5

no visible Drude peak

no sharp hybridization gap

F.P. Mena & D.Van der Marel, 2005

E.J. Singley & D.N Basov, 2002

second mid IR peakat 600 cm-1

first mid-IR peakat 250 cm-1

•At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) •At 10K:

•very narrow Drude peak•First MI peak at 0.03eV~250cm-1

•Second MI peak at 0.07eV~600cm-1

Optical conductivity in LDA+DMFT

CeIn

In

Multiple hybridization gaps

300K

e V

10K

•Larger gap due to hybridization with out of plane In•Smaller gap due to hybridization with in-plane In

non-f spectra

LDA+DMFT (10 K)LDA LDA+DMFT (400 K)

X M

X

XX

M

MM

g h

Fermi surface change with T

g h

Big change-> from small hole like to large electron like

1

Difference between Co,Rh,Ir 115’s

more localizedmore itinerantIr Co Rh

superconducting magnetically ordered“good” Fermi liquid

Total and f DOS f DOS

CeIn

In

X

•Commensurate AFM stable below ~3K•Moment has mainly

7

symmetry: moment lies in the ab

plane•Moment is ~1B

In exp:• AFM stable below 3.8K, but is spiral

Q=(1/2,1/2,0.298)a

•For B>3T, Q=(1/2,1/2,1/4)b

•Moment in plane!•Moment 0.26a,b, 0.59b, 0.75c B , 0.79 B

d

CeRhIn5 is most localized -> susceptible to long range magnetic order

a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000)b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007)c) Bao W et al, Phys. Rev. B 62 R14621 (2000)d) J. Thompson & T. Park, (2008)

Magnetism in CeRhIn5

Complex correlated matter holds a great promise for future technological materials

There is a lack of tools for describing complex correlated matter from first principles

Many aspect of complex matter physics are well described by DMFT

We have shown one such example: heavy fermion materials CeXIn5 Temperature crossover Spectral weight redistribution in momentum and

frequency Sensitivity to chemical substitution

ConclusionsConclusions

Thank you!

Iron superconductors, structure

Fe,Ni

As,P

La,Sm,Ce

O•2D square lattice of Fe•Fe - magnetic moment•As-similar then O in cuprates

But As not in plane!

Fe

As

Perfect tetrahedra 109.47°

Phonons give Tc<1KKH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)):

What is the glue?

L. Boeri, O. V. Dolgov, A. A. Golubov arXiv:0803.2703(PRL, 101, 026403 (2008)):

<0.21, Tc<0.8K

Y. Kamihara et.al.,

J. Am. Chem. Soc. 130, 3296 (2008).

Kink in resistivity

Not conventional superconductors!

Huge spin susceptibility (50 x Pauli)

Signatures of moments

Susceptibility 50xlarger than Pauli LDAT. Nomura et.al., 0804.3569

Doped LaOFeAsCaFe2As2 and Ca0.5Na0.5Fe2As2

Large restivity in normal state

Importance of Hund’s couplingHubbard U is not the “relevant” parameter.

The Hund’s coupling brings correlations!

Specific heat within LDA+DMFTfor LaO1-0.1F0.1FeAs at U=4eV

LDA value

For J=0 there is negligible mass enhancement at U~W!J~0.35 gives correct order ofMagnitude for both and The coupling between the Fe magnetic moment and the mean-field medium

(As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling!KH, G. Kotliar, cond/mat 0803.1279

LaO1-0.1F0.1FeAs

Common features of the parent c.

CaFe2As2 and Ca0.5Na0.5Fe2As2SmOFeAs

Structural transition & SDW

superconductivity

Enormous normal state resistivities!Very unusual

Structural transitionSDW not noticed

superconductivity

Variety of materials

CaFe2As2, (Tc=12K @ 5.5GPa), Milton S. Torikachvili, arXiv:0807.0616v2

Li1-xFeAs, (Tc=18K), X.C.Wang et.al., arXiv:0806.4688

FeAs layer

Ba or Ca

(Ba1-xKx)Fe2As2 (Tc=38K, x~0.4), Marianne Rotter et.al., arXiv:0805.4630

hole doped (not electron doped)

FeSe1-0.08, (Tc=27K @ 1.48GPa), Yoshikazu Mizuguchi et.al., arXiv: 0807.4315

No arsenic !

A. Kreyssig, arXiv:0807.3032

Bond angle seems to matter most. Perfect tetrahedra (109.47° ) -> higher Tc

R O1-xFx FeAs electron doped

BaFeAs2 (Tc=?)J.H. Shim, KH, G. Kotliar, arXiv: 0809.0041

S.C. Riggs et.al., arXiv: 0806.4011

SmFeAsO1-xFx

Phase diagrams SmFeAsO

A. J. Drew et.al., arXiv:0807.4876.

muon spin rotation magneto-transport experiments

Very similar to cuprates, log(T) insulator due to impurities

A. Kreyssig et.al, arXiv: 0807.3032

CaFe2As2 under pressure

Phase diagrams CaFe2As2

Volume collapse

Stoichiometric compound

Common features of the parent c.

CaFe2As2 and Ca0.5Na0.5Fe2As2SmOFeAs

Structural transition & SDW

superconductivity

Enormous normal state resistivities!Very unusual

Structural transitionSDW not noticed

superconductivity

Magnetic and structural PT

LaOFeAs

R. Klingeler et.al., arXiv:0808.0708v1

Clarina de la Cruz, Nature 453, 899 (2008).

In single crystals of 122 seems TM and TS close or the same

Tetragonal->Orth.

magnetic

arXiv:0806.3304v1

Fe magnetism ?Weak structural distortion ~150 K: from tetragonal to orthorombic

SDW (stripe AFM) at lower T Neutrons by: Clarina de la Cruz et.al, Nature 453, 899 (2008). top view

side view

But Iron Fe2+ has 6 electrons, [Ar] 3d6 4s0 and spin S=2.

Why is not μ larger?Why it varies so much?

LaFeAsO: TSDW~140K μ~0.3-0.4μB (a)

NdFeAsO: TSDW~1.96K μ~0.9μB/Fe (b)

(c) Huang, Q. et al., arXiv:0806.2776

SDW temperature and magnetic moment vary strongly between compounds:

(b) Jan-Willem G. Bo, et.al., arXiv:0806.1450

(a) Clarina de la Cruz et.al, Nature 453, 899 (2008).

BaFe2As2: T0~TSDW~100K μ~0.9μB/Fe (c)

SrFe2As2: T0~TSDW~205K μ~1.01μB/Fe (d)

(d) K. Kaneko et.al., arXiv: 0807.2608

Itinerancy & Frustration

Magnetic exchange interaction is very frustrated (Qimiao Si, Elihu Abrahams, arXiv:0804.2480)

For the doped compound, LDA structural optimization fails for non-magnetic state! (It is very good if magnetism is assumed)

For non-magnetic state, LDA predicts 1.34Å shorter FeAs distance (10.39 instead of 11.73).One of the largest failures of LDA.

T. Yildirim, arXiv: 0807.3936

The undoped compound is metal (although very bad one ~1mcm), hence moment is partially screened

Exchange interactions are such that J2~J1/2, very strong frustration,(KH, G. Kotliar, arXiv: 0805.0722)

Paramagnetic statemust have (fluctuating)magnetic momentsnot captured in LDA

Signatures of moments

Susceptibility 50xlarger than Pauli LDAT. Nomura et.al., 0804.3569

Doped LaOFeAs

Band structure of LaOFeAs

LDA: Mostly iron bands at EF (correlations important)

6 electrons in 5 Fe bands:Filling 6/10 -> large spin

LDA DOS

KH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)):

The 5-band Hubbard-type modelAs(p)-Fe(d) hybridization weak

Hoppings available at http://www.physics.rutgers.edu/~haule/FeAs/

LDA+DMFT: LaOFeAs is at the verge of the metal-insulator transition (for realistic U=4eV, J=0.7eV)For a larger (U=4.5, J=0.7eV) semiconducing insulator

Not a one band model: all 5 bands important (for J>0.3)

Need to create a singlet out of spin and orbit

DMFT for LaFxO1-xFeAs

Importance of Hund’s couplingHubbard U is not the “relevant” parameter.

The Hund’s coupling brings correlations!

Specific heat within LDA+DMFTfor LaO1-0.1F0.1FeAs at U=4eV

LDA value

For J=0 there is negligible mass enhancement at U~W!J~0.35 gives correct order ofMagnitude for both and The coupling between the Fe magnetic moment and the mean-field medium

(As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling!KH, G. Kotliar, cond/mat 0803.1279

LaO1-0.1F0.1FeAs

DMFT can describe crossover from local moment regime to heavy fermion state in heavy fermions. The crossover is very slow.

Mid-IR peak of the optical conductivity in 115’s is split due to presence of two type’s of hybridization

Ce moment is more coupled to out-of-plane In then in-plane In which explains the sensitivity of 115’s to substitution of transition metal ion

Fermi surface in CeIrIn5 is gradually increasing with decreasing temperature but it is not saturated even at 5K.

The out-of plane impurity hybridization (at 7K) is for 50% larger in CeIrIn5 than in CeRhIn5.

CeIrIn5 is most itinerant and CeRhIn5 most localized.

ConclusionsConclusions

Fermi surfaces of CeM In5 within LDA

Localized 4f:LaRhIn5, CeRhIn5

Shishido et al. (2002)

Itinerant 4f :CeCoIn5, CeIrIn5

Haga et al. (2001)

T decreasing

How does the Fermi surface change with temperature?

Electron fermi surfaces at (z=0)


X M

X

XX

M

MM

2 2

Slight increase of the

electron FS with decr T

R A

R

RR

A

AA

3

a

3


Electron fermi surfaces at (z=)No a in DMFT!No a in Experiment!

Slight increase of the

electron FS with decr T


X M

X

XX

M

MM

c

2 2

11

Electron fermi surfaces at (z=0)Slight increase of the electron FS

with decr T

R A

R

RR

A

AA

c

2 2


Electron fermi surfaces at (z=)No c in DMFT!No c in Experiment!

Slight increase of the electron FS

with decr T


X M

X

XX

M

MM

g h

Hole fermi surfaces at z=0

g h

Big change-> from small hole like to large electron like

1

Difference between Co,Rh,Ir 115’s


superconducting magnetically ordered“good” Fermi liquid

Total and f DOS f DOS

Mean field hybridization of Ce 4f electrons

in space:

the angular part:

at low frequency – we diagonalize:

The three important terms:

The origin of the difference: hybridization

In-plane hybridizationis small

•Ir largest,•Co next•Rh smallest

Out of-plane hybridizationIs large, difference important

•Ir largest•Co next•Rh much smaller

The distance to in-plane and out-of plane In is almost the same

In2

In1

Out-of plane hyb.very weak in Rh

Vanishing optical Hybridization gap!


superconducting magnetically ordered

“good” Fermi liquid

Distance between Ce and in-plane In:6.246 6.164 6.222

Distance between Ce and out-of-plane In:6.183 6.202 6.194

Angle 45° -0.59° 45° +0.35° 45° -0.26°

In(2): (1,0,1-0.02030)x4.4164 (1,0,1+0.01246)x4.3586 (1,0,1-0.00894)x4.3994

Distance of Ce-In(1,2)?

angleAngle=45°: In(1) and In(2) are at the same distance from Ce

It is not the structure, but the ion itself, that makes the difference!Difference between Co/Rh/Ir atom and not the structure is relevant.

The structure difference is the secondary effect.

•Commensurate AFM stable below ~3K•Moment has mainly

7

symmetry: moment lies in the ab

plane•Moment is ~1B

In exp:• AFM stable below 3.8K, but is spiral

Q=(1/2,1/2,0.298)a

•For B>3T, Q=(1/2,1/2,1/4)b

•Moment 0.26a,b, 0.59b, 0.75c B , 0.79 Bd


CeRhIn5 is most localized -> susceptible to long range magnetic order

a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000)b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007)c) Bao W et al, Phys. Rev. B 62 R14621 (2000)d) J. Thompson & T. Park, (2008)

Fe,Ni

As,P

La,Sm,Ce

O

SmFeAsO1-xFx

New Iron high-Tc’sThursday 14. August, afternoon (2:30-…)

Frequency dependence of hybridization

Substantial differenceCoherence scale exponentially sensitive to hybridization

Relative importance of atomic states

N=1N=0

Probability to find electron in one of the atomic states (CeIrIn5)

most important

20% lower p.

10% less

empty 10% less


CeRhIn5 shows a clear signature of a Kondo peak above TNell

Kondo screening relatively poor compared to other two 115’sNell state develops out of partly localized/itinerant state

Fujimori 2006Rh has a small hump

dHva freq. and effective mass

300K

10K5K

DMFT is not a single impurity calculation

Auxiliary impurity problem:

High-temperature given mostly by LDA

low T: Impurity hybridization affected by the emerging coherence of the lattice

(collective phenomena)

Weiss field temperature dependent:

Feedback effect on makes the crossover from incoherent to coherent state very slow!

high T

low T

DMFT SCC:

Nonmagnetic impurities not detrimental to SC

BaFe1.8Co0.2As2: Tc~22K

•Fe replaced by Co •Impurities do not destroy SC (like Zn doping in cuprates)•No signature of Curie-Weiss susc.

F.L. Ning et.al, arXiv:0808.1420

V2O3Ni2-xSex organics

Universality of the Mott transitionUniversality of the Mott transition

First order MITCritical point

Crossover: bad insulator to bad metal

1B HB model 1B HB model (DMFT):(DMFT): B

ad in

sula

tor

Bad metal1B HB model 1B HB model (plaquette):(plaquette):

DMFT for a simple systemDMFT for a simple system

Identify correspondence between the local and impurity quantities:

Identify correspondence between the local and full GF:

Solve QIM:

Equivalent to summation of all local Feynman diagramsA. Georges & G. Kotliar, RMP 1996

Iron SC: How it all started….

Published in Chemical journal (Journal of American Chemical Society)Received January 2008, published online Feb 2008

And exploded….more than 23 cond-mat’s in March 2008

>260 preprints at the end of July mostly from China!

R=(0,0) R=(1,0)

R=(1,1)

Reference systemsReference systems

Reference system in DFT: Kohn-Sham system of independent electrons

Reference system in DMFT: One interacting atom + system of independent electronsInteracting cluster+ system of independent electrons

Kohn-Sham: Potential is local and static

Self-energy is short ranged and retarded

Obtained by solving a QIM

Documents

Predicting and Understanding Correlated Electron Materials: A Computational Approach