Introduction to correlated materials, DFT, DMFT DFT +DMFT · of electronic structure of strongly...
Transcript of Introduction to correlated materials, DFT, DMFT DFT +DMFT · of electronic structure of strongly...
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
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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…
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•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.
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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……
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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.
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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.
THE STATE UNIVERSITY OF NEW JERSEY
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.
THE STATE UNIVERSITY OF NEW JERSEY
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.
THE STATE UNIVERSITY OF NEW JERSEY
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 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
THE STATE UNIVERSITY OF NEW JERSEY
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.
THE STATE UNIVERSITY OF NEW JERSEY
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
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
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
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
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 ?
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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
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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)
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