Introduction to correlated materials, DFT, DMFT DFT +DMFT · Determine energy and and self...

Introduction tocorrelated materials,

DFT DMFT DFT +DMFTDFT, DMFT, DFT +DMFT, etc.

Gabriel KotliarGabriel KotliarRutgers University

New Trends in Computational Approaches for Many Body SystemsBody Systems.

Quebec May 30 2011

Conceptual Basis of the LDA+DMFTh d h h d hmethod has not changed much.

Talked based on early lecture notes G Kotliar andTalked based on early lecture notes. G. Kotliar and S. Savrasov in New Theoretical Approaches to Strongly Correlated G Systems, A. M. Tsvelik Ed. g y y ,

2001 Kluwer Academic Publishers. 259‐301 . cond‐mat/0208241

• Dramatic Progress in Implementation g phas resulted in major advances in the physics of strong correlations.

Formal introductionFormal introductionto effective actions for electronic

structure.

Spectral density functional. Effective action construction.e.g Fukuda et.al

[ ] [ ( ) ]F J S JAZ e d d e y yy y+- + - += = ò

et.al

Z e d d ey y= = ò[ ]F J A a

Jdd

=< >=Jd

[ ] [ [ ] ] [ ]a F J a aJ aG = -

0 intS S Sl= +0 int

J J Jl= + +0 1J J Jl= + +

[ ]aG = 0G1l+ G +[ ]a+DG0 0 0[ ]F J aJ-

DG G Ghartree xcDG=G +G

1

int

0

[ ] ( , ( , ))a d S J al l lDG = < >ò0

In practice we need good approximations to the exchangeIn practice we need good approximations to the exchange correlation, in DFT LDA. In spectral density functional theory, DMFT. Review: Kotliar et.al. Rev. Mod. Phys. 78, 865 (2006)

dDGFd0[ ]J a

addDG

=00

[ ]F J aJdd

=ad0Jd

Kohn Sham equations

Remarks:E t f ti l f b bl A• Exact functionals of an observable A,

• In practice approx are needed[ ]exact aG

[ ] [ ]mft exacta aG G• Many a’s many theories. • Introduction of a reference system. Separation into y p“free part” and exchange+ correlation. •Formal expression for the correlation part of the exact functional as a coupling constant integration. •Good approximate functionals obtained by approximating the xc part [ small parameter dapproximating the xc part. [ small parameter d helps!]• While the construction aims to calculate <A>=a,While the construction aims to calculate A a, other quantities, e.g. correlation functions, emerge as a byproduct [bands, correlation functions…... ]

Crucial Role of the constraining fieldDifferent reference systems [ e g

0 [ ]J aDifferent reference systems [ e.g. band limit or atomic limit ] define different constraining fields.

Diff t f ti l ( lf f ti l• Different functionals (self energy functional, BK functional, Harris Foulkes functional, etc )

[ ] [ ] [ ] [ ]J J JG G G G0 0[ ], [ , ], [ , ], [ ]a a J a J JG G G G

Density functional and Kohn Sham f t

[ ]

reference system

2 / 2 ( ) KS kj kj kjV r y e y- + =2( ) ( ) | ( ) |f yå

( ') Er drò

2( ) ( ) | ( ) |kj

kj kjr f rr e y=å( )( )[ ( )] ( ) ' [ ]

| ' | ( )xc

KS extErV r r V r dr

r r rdr

r rdr

= + +-ò

•Kohn Sham spectra, proved to be an excellent starting point for doing perturbation theory in g p g p y

screened Coulomb interactions GW.

LDA+DMFT unifies physics and hchemistry

• Treat both band physics and atomic physics.• Hubbard bands and Quasiparticle bands.• Combine Model Hamiltonians insights with realistic b d t t f l t i lband structure of complex materials.

• Makes many body theory system specific, analysis of chemical trends.chemical trends.

• Simplest approach merging previous success stories. • XC : [ ] [ , ]uniformgas locatom f dc atomfGr r- -DG +DG -DG

• Allows the solution of many intersting problems.• Many improvements are possible.

f f

Why can we even contemplate now the possibility of material design (in weakly correlated electron systems)?

Success based on having a good reference system d ib h l h i / i l

“Standard Model” of solids developed in the

to describe the relevant physics / materials.

Standard Model of solids developed in the twentieth century. Reference System:Freel t i i di t ti l

W k ll( f kl l t d

electrons in a periodic potential.

Works well( for very weakly correlatedmaterials), e.g. simple metals and insulators

6

Band Theory. Fermi Liquid Theory (Landau 1957).

Density Functional Theory (Hohenberg Kohn Sham 1964)

2 / 2 ( )[ ]V r r y e y + = Reference Frame for / 2 ( )[ ] KS kj kj kjV r r y e y- + = Weakly Correlated Systems.

( ) *( ) ( )kj kjr r rr y y= åExcellent binding energies and structures /Starting point for perturbation theoryGW (Hedin) in the screened Coulomb interactions

0( ) ( ) ( )

kjkj kje

r y y<å

+ [ - ]KSV10KSG1G

M. VanSchilfgaarde Phys. Rev. Lett. 93, 126406 (2004)

[ ]KS0KS

Many other properties can be computed, structure , transport, optics, phonons, etc…

7

•The “standard model” fails for strongly correlated electron materials.• Results in “big things”. Metal to insulator transitions, heavy fermion behavior, high y gtemperature superconductivity, colossal magnetoresistance, giant thermolectricity …………..•The Kohn Sham system cannot possibly describe spectroscopic properties of correlated materials, because these retain atomic physics aspects (Motness, e.g. multiplets, transfer or spectral weight, high Tc’s, ) which are not perturbative•NEEDED: a new reference system to describe correlated materials.

8

Strongly correlated materials do “big” thingsCompetition of localization and itineracyCompetition of localization and itineracy.

• Huge volume collapses in lanthanides and actindies, eg. CeHuge volume collapses in lanthanides and actindies, eg. Ce, Pu, …….

• Metal insulator transitions as a function of pressure an composition in transition metal oxides VO2 V2O3composition in transition metal oxides, VO2 V2O3

• Quasiparticles with large masses m* =1000 mel in Ce and U based heavy fermions.y

• Colossal Magnetoresistance in La1‐xSrxMnO3• High Temperature Superconductivity. 150 K Ca2Ba2Cu3HgO8.

• Large thermoelectric response in NaxCo2O4 • 50K superconductivity in SmO1‐xFxFeAs50K superconductivity in SmO1 xFxFeAs • Many others……

55

DYNAMICAL MEAN FIELD THEORY :View solid as collection of atoms or clusters in a self consistent medium [ Quantum Impurity Model ] A. Georges and G. Kotliar PRB 45,6479 (1992)A reference frame for thinking about and computing the properties of correlated materialsproperties of correlated materialsFormulated as a first principles approach. DFT+DMFT[V. Anisimov A. Poteryaev M. Korotin A. Anokhin and G. Kotliar.

Exact in infinite dimensions Metzner and Vollhardt PRL 62,

Anisimov A. Poteryaev M. Korotin A. Anokhin and G. Kotliar.J Phys. Cond. Mat 35, 7359 (1997).

How can we tell if and when a local approach is OK ?Cluster DMFT Studies CDMFT kotliar et al Phys Rev Lett

324 (1989) Kinetic energy ~ onsite repulsion

Cluster DMFT Studies. CDMFT kotliar et. al. Phys. Rev. Lett. 87, 186401 (2001). DCA M Hettler et. al. Phys. Rev. B 58, 7475 (1998)( )Compare experiments with multiple theoretical and experimental spectroscopies.

9

Functional formulation. Chitra and Kotliar (2001), Ambladah et. al. (1999) ( )

Savrasov and Kotliarcond‐matt0308053 (2003).

1 †1 ( ) ( ') ( ') ( ) ( ) ( )V if f f y y-+ +ò ò ò1 †( ) ( , ') ( ') ( ) ( ) ( ) 2

Cx V x x x i x x xf f f y y-+ +ò ò ò

†( ') ( ')G R Ry r y r=-< > ( ') ( ) ( ') ( )R R R R Wf r f r f r f r< >-< >< >=Ir>=|R, >1 1 1 1

01 1[ ] [ ] [ ] [ ]C hG W TrLnG Tr G G G TrLnW Tr V W W E G W

[ ] [ 0 0]G W G W G W

0[ , ] [ ] [ ] [ , ]2 2 C hartreeG W TrLnG Tr G G G TrLnW Tr V W W E G W

D bl l i Gl d Wl

THE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

[ , ] [ , , 0, 0]EDMFT loc loc nonloc nonlocG W G W G W Double loop in Gloc and Wloc

Two paths for ab‐initio calculation pof electronic structure of strongly

correlated materialscorrelated materials

Crystal structure +Atomic positions

Model Hamiltonian

Correlation Functions Total Energies etc.


RUTGERSMean field ideas can be used in both cases.

Model HamiltoniansModel Hamiltonians

• Tight binding form.• Eliminate the “irrelevant” high energy degrees of freedom

• Add effective Coulomb interaction termsAdd effective Coulomb interaction terms

One Band Hubbard modelOne Band Hubbard model

† †( )( )t c c c c U n n , ,

( )( )ij ij i j j i i ii j i

t c c c c U n n

U/t

Doping or chemical potential

Frustration (t’/t)

T temperatureMott transition as a function of doping, pressure temperature etc.

Extension to clusters. Cellular DMFT. C‐DMFT. G. Kotliar,S.Y. Savrasov G Palsson and G Biroli Phys Rev Lett 87 186401 (2001)Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001)

tˆ(K) i th h i d i th tˆ(K) is the hopping expressed in the superlattice notations.

•Other cluster extensions (DCA, nested cluster schemes, PCMDFT ), causality issues, O. Parcollet, G. Biroli and GK ), y , ,

cond-matt 0307587 (2003)

Dynamical Mean Field Theory. Cavity Construction.A. Georges and G. Kotliar PRB 45, 6479 (1992).

,ij i j i

i j i

J S S h S- -å å† †( )( )t c c c c U n n

† † † † †Anderson Imp 0 0 0 0 0 0 0( +c.c). H c A A A c c UcV c c c † †

, ,

( )( )ij ij i j j i i ii j i

t c c c c U n n

p 0 0 0 0, , ,

*V VA(A())

†

0 0 0

( )[( ) ( '' ] '))( ) (o o o oc c U n nb b b

s st tt m d t t tt D¶

+ - - +¶

-ò ò ò( ) V Va a

a a

ww e

D =-å

(( ))

77

latt ( , 1 G [ ]( ) [( ) ]

)[ ]n imp

nn

ik ii

ktw m

ww+ + -S

DD

=

( )wDA(A()) Solving A for given bath, is not easy Impurity solvers; See other lectures i h l O S O OG SSS

[ ]ijij

jm mJth hb= +å 1( )[ ]( )

( )[ ]imp n

n n ni i iG iw

w w wD +DD

-S -

in school, LOTS OF PROGRESSS

( )[ ]imp n

1latt( )[ ] ( ) G ( , )n nni i it k kw w m w --S D - + =

latt( ) G ([ [)] ] ,imp n nk

G i i kw wD D=å 88

LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar J Phys Cond Mat 35 7359 (1997)Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997).

A Lichtenstein and M. Katsnelson PRB 57, 6884 (1988).

• The light, SP (or SPD) electrons are extended, well described by LDA .The heavy, D (or F) electrons are localized treat by DMFT.

• LDA Kohn Sham Hamiltonian already contains an average interaction of the heavy electrons, subtract this out by shifting the heavy level (double counting term)out by shifting the heavy level (double counting term)

Kinetic energy is provided by the Kohn Sham Hamiltonian (sometimes after downfolding ). The U matrix can be estimated from first principles of viewedmatrix can be estimated from first principles of viewed as parameters. Solve resulting model using DMFT.


RUTGERS

Many Groups are Active in this Area. Implemented in all sorts of basis setsp

Very incomplete list.

LAPW

KKR

Plane waves

Plane waves

LAPW

Many Moving Parts…. Basis set, impurity solvers available, techniques for doing k sums, etc…techniques for doing k sums, etc…

Still main question is choice of projector. Clear description of the issues in a well tested dataset:

LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar J Phys Cond Mat 35 7359 (1997)Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997).

A Lichtenstein and M. Katsnelson PRB 57, 6884 (1988).

• The light, SP (or SPD) electrons are extended, well described by LDA .The heavy, D (or F) electrons are localized treat by DMFT.

• LDA Kohn Sham Hamiltonian already contains an average interaction of the heavy electrons, subtract this out by shifting the heavy level (double counting term)out by shifting the heavy level (double counting term)

Kinetic energy is provided by the Kohn Sham Hamiltonian (sometimes after downfolding ). The U matrix can be estimated from first principles of viewedmatrix can be estimated from first principles of viewed as parameters. Solve resulting model using DMFT.


RUTGERS

1( )G k i

LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997).

( , )( ) ( )

G k ii t k i

Spectra=‐ Im G(k,)

0 0æ ö0 00 ff

æ ö÷ç ÷S ç ÷ç ÷ç Sè ø

abcdU U, ,[ ] [ ]

( )[ ] [ ]

spd sps spd fH k H kt k

H k H kæ ö÷ç ÷ç ÷ç ÷ç

,[ ] [ ]f spd ffH k H kç ÷çè ø

| 0 ,| , | , | | ...JLSJM g> > > > >| 0 ,| , | , | | ...JLSJM g> > > > >

Determine energy and andDetermine energy and and self consistently from self consistently from extremizingextremizing a a functional functional ChitraChitra and and KotliarKotliar (2001) . (2001) . SavrasovSavrasov and and KotliarKotliar (2001) Full self (2001) Full self ( )( ) ( )( )consistent implementation consistent implementation

1212,[ ] [ , ]dft lda dmf loct G Ur r+G ¾¾ G

LDA+DMFT Self-Consistency loop

2| ( ) | ( )k xc k LMTOV H ka ac r c- + = E

G0 GImpuritySolver

S.C.C.

U

0( ) ( ) ir T G r r i e wr w+å

DMFT

0i +åTHE STATE UNIVERSITY OF NEW JERSEY

RUTGERS

( ) ( , , )i

r T G r r i ew

r w= å 0( , , )H Hi

H Hi

n T G r r i e w

w

w+

= å

LDA+DMFT functional[ ( ) G V ( ) ]

2 *lo g [ / 2 ( ) ( ) ]R R Rn K ST r i V r ra b baw c c- + - - S -

åò

KS ab [ ( ) G V ( ) ]LDA DMFT a br r

( ) ( ) ( ) ( )

1 ( ) ( ')( ) ( ) ' [ ]2 | ' |

n

K S n ni

L D Ae x t x c

V r r d r T r i G i

r rV r r d r d r d r E

w

r w w

r rr r

- S +

+ + +

åò

ò ò2 | ' |

[ ]R

e x t x c

D CR

r r

G ba

-

F - F

ò òå

Sum of local 2PI graphs with local U matrix and local G

1[ ] ( 1)2DC G Un nF = - ( )0( ) i

ababi

n T G i ew

w+

= å


RUTGERS

Based on work with Chitra and Savrasov

Embedding ˆ HHS S

ˆ LL LH

HL HH

H HH

H Hé ùê ú= ê úë û

22

11

0 0 0ˆ 0 0HH

HH

é ù é ùSê ú ê úS = S=ê ú ê úS Së û ë û

1ˆ ˆˆ ˆ( ) ( ) ˆ ˆˆ ˆ( ) ( )n k ni O H k E iO k

w w- - -S S

HL HHH Hë û110 0 HHS Së û ë û

I i ( ) ( )( ) ( )n k n

n k ni O H k E iw w- - -S

I t ti BZ1ˆ ( )lG iw =å

Inversion

0 0G G

é ùê ú=

Integrating over BZ

Truncation

( ) ˆ ˆˆ ˆ( ) ( )loc n

n k nk

G ii O H k E i

ww w

=- - -Så

0loc HH

HH

G GG

ê ú= ê úë û

1 1

Truncation

1 10 ( ) ( )HH HHn nG i G iw w- -= +S

LDA+DMFT depends on the choice of projector Central Concepts Embeddingprojector. Central Concepts. Embedding

and Truncation. P j i• Projection or Truncation E

• Embedding

LDA+DMFT is in principle Basis Set INDEPENDENT if h b i i d hif the basis set is good enough.BUT it depends on the choice of projector P. And different basis sets go with different projectors….

What is U in a solid ? Kutepov HauleWhat is U in a solid ? Kutepov HauleSavrasov Kotliar

Double CountingDouble Counting

Comments on LDA+DMFTComments on LDA+DMFT• Static limit of the LDA+DMFT functional , with = HF

reduces to LDA+U• Removes inconsistencies and shortcomings of this

approach DMFT retain correlations effects inapproach. DMFT retain correlations effects in the absence of orbital ordering.

• Only in the orbitally ordered Hartree Fock limit, the Greens y y ,function of the heavy electrons is fully coherent

• Gives the local spectra and the total energy simultaneously, treating QP and H bands on the same footing.


RUTGERS

Functional formulation. Chitra and Kotliar (2001), Ambladah et. al. (1999) Savrasov and(2001), Ambladah et. al. (1999) Savrasov and

Kotliarcond‐matt0308053 (2003).

1 †1 ( ) ( ') ( ') ( ) ( ) ( )V if f f y y-+ +ò ò ò1 †( ) ( , ') ( ') ( ) ( ) ( ) 2




[ ] [ 0 0]G W G W G W


D bl l i Gl d Wl


RUTGERS


Diagrams: PT in W and G. 1 11 1 1 1

01 1[ , ] [ ] [ ] [ , ]2 2 C hartreeG W TrLnG Tr G G G TrLnW Tr V W W E G W

Introduce projector GlocWlWloc

Many Body Perturbation Theory in G and W.

Order in Perturbation Theory

Order in PTn=1

Basis set i

l=1

n=2

size. DMFT

r site CDMFTl=2

r=1

r=2

GWl=lmax

r=2

GW+ first vertex correction

Range of the clusters

Outline for my (hopefully pedagogical) lectures. •• 2]Intuitive Derivation of Dynamical Mean Field Theory in model hamiltonian [Ease the reading ofTheory in model hamiltonian [Ease the reading of RMP] A. Georges G.Kotliar, W.Krauth & M.RozenbergRev Mod Phys 68 (1996) 13 Light reading G Kotliary ( ) g gand D Vollhardt Physics Today 57, 53‐59 (2004)

• Intuitive Derivation of LDA+DMFT • 1] Formal Derivations using functionals. [ Ease the reading of RMP ]

• Some motivating examples. • Next Lecture: Practical Implementation in ab‐init by Bernard Amadon.

Functional formulation. Chitra and Kotliar (2001), Ambladah et. al. (1999) Savrasov and(2001), Ambladah et. al. (1999) Savrasov and

Kotliarcond‐matt0308053 (2003).

1 †1 ( ) ( ') ( ') ( ) ( ) ( )V if f f y y-+ +ò ò ò1 †( ) ( , ') ( ') ( ) ( ) ( ) 2




[ ] [ 0 0]G W G W G W


D bl l i Gl d Wl


RUTGERS


EDMFT loop G. Kotliar and S. Savrasov in New Theoretical Approaches to Strongly Correlated G Systems, A. M. Tsvelik Ed. 2001 Kluwer Academic Publishers. 259‐301 . cond‐mat/0208241 S. Y. Savrasov, G. Kotliar, Phys. Rev. B 69, 245101 (2004)

Input: ,M PSpectral Density Functional Theory withinLocal Dynamical MeanFieldApproximation

Input: ,M PSpectral Density Functional Theory withinLocal Dynamical Mean Field Approximation

/ , , y , ( )

1 10 lG G M

1( )loc

k

GH k

M

Local Dynamical Mean Field Approximation

,loc locG W 1 10 locG G M

1( )

1

lock

GH k

M

y pp

01 1

0

loc

loc

G

W

G MV P

1

1( )loc

q C

Wv q

P

1 10 locW V P

1

1( )loc

q C

Wv q

P

G VM P0 0G V,,intM P

Local Impurity Model

Output: Self-Consistent Solution

0 0G V,,intM PLocal Impurity Model

Output: Self-Consistent Solution

•Full implementation in the context of a a one orbital model. P Sun and G. KotliarPhys. Rev. B 66, 85120 (2002).

•After finishing the loop treat the graphs involving Gnonloc Wnonloc in perturbation theory. P.Sun and GK PRL (2004). Related work, Biermann Aersetiwan and Georges PRL 90,086402 (2003) .

An Aside (K. Haule lectures)…… Hybrids

Rare earth oxides and sulfides are studied because of its t l ti ti d i t ll f i dl i tcatalytic properties and as enviromentally friendly pigments.

Schematic DOS of R2O3

La O

Ce 4f

Schematic DOS of R2O3

La2O3

O 2p

Ce 5dpd gap

Ce2O3 Mott gap Upper Hubbard

Position of the f band in

pd gapf band

Position of the f band in any static mean field theory when symmetry is not broken

Hybrid + DFT Good agreement with experiments without adjusting parameters. Suggestion alpha in the hybrid x Vc =U . Edc, substract exchange contribution in hybrid only.

Example: rare earth sesquioxides. Ce2O3

Hybrid + DFT Good agreement with experimentsHybrid + DFT Good agreement with experiments without adjusting parameters. Suggestion alpha in the hybrid x Vc =U . Edc, substract exchange contribution in hybrid only.

Comparisons of the methods G0W0 [LDA+U]Phys. Rev. Lett. 102, 126403 (2009)

H,Jiang, R. Gomez‐Abal, P Rinke, M. Scheffler

Discovery of superconductivity in Fe l 7layers. 7

Predictive power of realistic DMFT and its extensions. .

Hosono et.a.., Tokyo, JACS (2008)

Address Predictive power of state of the art methods

Iron Pnictides: correlation stregnth ?

• LDA calculation. D. J Singh and M.H. Du Phys. Rev. Lett. 100, 237003 (2008), I. Mazin, M. Johannes and collaborators. Itinerant magnets.

• LDA should be corrected by long wavelength fluctuations effects. LDA overestimate of moment due to proximity to quantum critical point. Include fluctuating twin and antiphase domain boundaries.

• Haule K, Shim J H and Kotliar G Phys. Rev. Lett. 100, 226402 (2008). Parent compounds correlated multiorbital bad semi‐metals” U< Uc2, m*/m~3‐5). small crystal –fields.

• Band theory should be supplemented by local correlations to capture local quantum fluctuations. LDA+DMFT +extensions correlations are implemented via F0 F2 F4 applied to a set of orbitals (projector)

l d f f d b h h• Localized point of view, magnetic frustration. Q.Si and E.Abrahams Phys. Rev. Lett. 101, 076401. (2008).

• Extension of the t‐J model to S=2 multiorbital situation.Different views suggest different theoretical approaches Different reference systems to thinkDifferent views suggest different theoretical approaches. Different reference systems to think about and compute the properties of materials. Which one is more accurate ?

11

Early DMFT predictionsEarly DMFT predictionsy py p

Generic values of U , 4 ev, and J =.9 ev , orbital built on a 4 ev window 14

Unconventional SCPhonon Tc<1K

Importance of correlationsImportance of correlationsMass enhancement 3‐5

Small X‐field splittings

Hunds metals not doped Mott insulators , Strength of correlations are due to Fe Hunds rule J not to Hubbard U. K. Haule and G. Kotliar cond‐mat arXiv:0805.0722New Journal of Physics 11 (2009) 025021

U=5ev

1515

LDA valueOrbital blocking. In d6 configuration exponential amplification is regulated by x‐'.Kondo k kH J d d c cab a b a bs s+ +=å p p g y

fields. Very different than oxides. , 'k ka bå

J J

J Jab

d

=

=

1JN

KNJ

T e r

r

-

-

=

Work by other DMFT groups Liebsch andJ Jab abd= JKT e r= Work by other DMFT groups. Liebsch and

Ishida, Aichorn et. al.P. Hansman …. Sangiovanni and Held Phys. Rev. Lett. 104, 197002 (2010)

pnictide/chalcogenide 17

Are these a new class of strongly correlated electron systems ?

K Fe Se

Ishida Nasai and HOsonJ. Phys. Soc. Jpn. 78

Paglione and Greene Nature Physics 6, 645(2010)

K1‐xFe2‐2xSe2 (2009) 062001

Hunds metals not doped Mott insulators , Strength of correlations are due to Fe Hunds rule J not to Hubbard U. K. Haule and G. Kotliar cond‐mat arXiv:0805.0722New Journal of Physics 11 (2009) 025021

U=5ev

1818

LDA value

N ki d f l l d lNew kind of strongly correlated electron system. Coherence Incoherence Crossover. as a function fof temperature.

Beyond the localize vs itinerant dichotomy.

Freq. dep. U matrix applied to localized Fe d orbital, (12 i d ) W ll t i d b F0 F2 F4(12 ev window) Well parametrized by F0 F2 F4

After the constrained RPA

But with the self consistent GW input andinput and adopting a local perspective Kutepov et. al.

F0 4:9 eV F2 6:4 eV and F4 4:3 eV nc 6 2F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV., nc=6.2

19

M. Moment & Optics by LDA+DMFT 22

Z. Yin, Khaule , G Kotliar, Nature Physics (2011).Exp moment: 0.87 µB

LDA+DMFT moment: 0.9 LDA

moment 2µB

Correct plasma ωp:DMFT ~ 1.6eVExp ~ 1.6eVLDA ~ 2.6eV

3 peak structure beyond SDWbeyond SDW

Experiment: W. Z. Hu, et al, PRL 101, 257005 (2008).Nakajima, M. et al. Phys. Rev. B 81, 104528 (2010).

Anisotropy of the conductivity d dpredicted.

Z. Yin K. Haule and GK Nature Physics 7, 294‐297 (2011)

Experiment:M. Nakajima, …,S Uchida, PNAS 108, 12238 (2011) DiGiorgi EPL (2011)

23

THE ENDTHE ENDThanks for your attention!!!!!Thanks for your attention!!!!!

Hope it raised your interest and you want toHope it raised your interest and you want to contribute so that we can have a predictive theory of correlated materials in the very nearof correlated materials in the very near future……….

Interested in positions, contact me at

[email protected]

Introduction to correlated materials, DFT, DMFT DFT +DMFT · Determine energy and and self...

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Transcript of Introduction to correlated materials, DFT, DMFT DFT +DMFT · Determine energy and and self...