Ab-initio theory of the electronic structure of strongly correlated materials: examples from across the periodic table.

G.Kotliar Physics Department Center for Materials Theory

Rutgers University.

September 27-29 (2007) Tokyo Japan

COE 21 Workshop Applied Physics on Strong Correlation

Outline

• Electronic structure properties of correlated materials, the first principles DMFT strategy.

• sp Si semiconductors

• 4f Ce 115’s

• 5f elemental actinides

• 3d cuprate superconductors

Chitra and Kotliar PRB 62, 12715 (2000) PRB 63, 115110 (2001)  

Ir,>=|R, > Gloc=G(R, R’ ’ ) R,R’

Introduce Notion of Local Greens functions, Wloc, Gloc G=Gloc+Gnonloc .

Electronic structure problem: compute <r|G|r’> and <r|W|r’> given structure

[ , ] sum all 2PIgraphs= +

+

G W

G

DMFT mapping: site or cluster of sites in a self consistent medium. Quantum impurity solver, gives and P.

LDA+DMFT . V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997) Review: G. Kotliar S. Savrasov K Haule O Parcollet V Oudovenko C. Marianetti RMP (2006)

Approximate the self energy of a subset “ uncorrelated electrons “ by the LDA Vxc(r)(r,r’) replace W() by a static U acting only the “correlated “ set, treated by DMFT.

“ Local” can mean a small cluster of sites or multiple unit cells. Cellular DMFT, cluster DMFT.

Silicon. Correlations on sp electrons. First order PT as impurity solver. [Cluster version of GW] LMTO ASAbasis set. F. Aryasetiawan and O. Gunnarson, Phys. Rev. B 49, 16 214 (1994). Convergence as a function of size.

Zein Savrasov and Kotliar PRL 96, 226403 (2006)

expt-gap 1.17 Theory .9expt bandwidth: 12.6 theory 13.7

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.04

0 1 2

Sigma s GW

Sigma p GW

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0 1 2

D Sigma s

D Sigma p

GW self energy for SiSelf energy corrections beyond GW

Coordination Sphere Coordination Sphere

Locality of correlations Zein Savrasov and GK PRL 96, 226403 (2006))

Similar conclusion for other materials, Na, Al, Fe Ni……..

CeRhIn5: TN=3.8 K; 450 mJ/molK2 CeCoIn5: Tc=2.3 K; 1000 mJ/molK2; CeIrIn5: Tc=0.4 K; 750 mJ/molK2

4f systems. CeMIn5 M=Co, Ir, Rh

out of plane

in-plane

Ce

In

Ir

Angle integrated photoemission

Experimental resolution ~30meVSurface sensitivity at 122 ev , theory predicts 3meV broad band

Expt Fujimori et al., PRB 73, 224517 (2006) P.R B 67, 144507 (2003).

Theory: LDA+DMFT, impurity solvers SUNCA and CTQMC Shim Haule and GK (2007)

Very slow crossover!

T*

Slow crossover more consistent with NP&F

T*

cohere

nt

spect

ral

weig

ht

T

NP&F: Nakatsuji,Pines&Fisk, 2004

Buildup of coherence in single impurity case

TK

cohere

nt

spect

ral

weig

ht

T

scattering rate

coherence peak

Buildup of lattice coherence

Crossover around 50K

Momentum resolved total spectratrA(,k)

Fujimori, PRB

LDA+DMFT at 10K ARPES, HE I, 15K

LDA f-bands [-0.5eV, 0.8eV] almostdisappear, only In-p bands remain

Most of weight transferred intothe UHB

Very heavy qp at Ef,hard to see in total spectra

Below -0.5eV: almost rigid downshift

Unlike in LDA+U, no new band at -2.5eV

Short lifetime of HBs -> similar to LDA(f-core)rather than LDA or LDA+U

•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

Expts: F. P. Mena, D. van der Marel, J. L. Sarrao, PRB 72, 045119 (2005).16. K. S. Burch et al., PRB 75, 054523 (2007).17. E. J. Singley, D. N. Basov, E. D. Bauer, M. B. Maple, PRB 65, 161101(R) (2002).

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

after G. Lander, Science (2003)and Lashley et. al. PRB (2006).

Mott Transition

PuPu

Mott transition across the actinides. B. Johansson Phil Mag. 30,469 (1974)]

Pu phases: A. Lawson Los Alamos Science 26, (2000)

GGA LSDA predicts Pu to be magnetic with a large moment ( ~5 Bohr) . Experimentally Pu is not magnetic. [PRB 054416(2005). Valence of Pu is controversial.

DMFT Phonons in fcc DMFT Phonons in fcc -Pu-Pu

  C11 (GPa) C44 (GPa) C12 (GPa) C'(GPa)

Theory 34.56 33.03 26.81 3.88

Experiment 36.28 33.59 26.73 4.78

( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003)

(experiments from Wong et.al, Science, 22 August 2003)

What is the valence in the late actinides ?

3d’s High Tc Superconductors

Does a plaquette DMFT of simple model Hamiltonians, (Hubbard and t-J) , capture the qualitative physics of cuprates ?

Doping driven Mott transition in 2d-single band spin 1/2 system.

Study different mean field phases as a function of parameters.

Avoid the hard controversial question of which phase has the lowest free energy in the thermodynamical limit. cf Maier et. al. 95, 237001 (2005)Aimi and Imada arXiv:0708.3416

Doping Driven Mott transiton at low temperature, in 2d (U=16 t=1, t’=-.3 ) Hubbard model

Spectral Function A(k,ω→0)= -1/π G(k, ω →0) vs kK.M. Shen et.al. 2004

2X2 CDMFT

Nodal Region

Antinodal Region

Civelli et.al. PRL 95 (2005)Civelli et.al. PRL 95 (2005)

Senechal eta. PRL 94 (20050Senechal eta. PRL 94 (20050

Nodal Antinodal Dichotomy and pseudogap.

Superconducting Nodal

quasiparticles

Antinodal gap M. Civelli, cond-mat 0704.1486G. Kotliar and K Haule PRB (2007)

Anomalous self energy contribution has

a dome like shape (like v)

Normal self energy contribution monotonically decreasing

Kondo Takeuchi Kaminski Tsuda and shin, PRL 98, 267004 (2007).Tanaka et. al. Science 315 , 1910 (2006)Kanigel et.al. PRL (2007)

Photoemission expts ?

Thanks!• SP electrons. Zein Savrasov and GK PRL 96,

226403 (2006)• Ir 115 J. Shim K. Haule and GK (2007)• Pu. K Haule J Shim and GK . Nature 446,

513, (2007)• High Tc’s. Groups in Canada, France , Rome

and Rutgers. M. Civelli, cond-mat 0704.1486 K Haule and GK PRB (2007)

Support from NSF-DMR and DOE-BES

First priciples theory assisted material design with correlated

electron systems ?

• Are we there yet ?

• No………, but wait!!!!!

.Smallest cell which captures the physics of the solid. .Impurity solver to obtain the self energy of the strongly correlated and weakly correlated electrons.

Conclusions

• Correlations in sp electrons (worse case ) require 3 coordination spheres.

• 4f’s single site works reasonably well for the Ir 115. Quantum critical point : 2 site DMFT ?

• 5f’s Pu as a mixed valent metal. Cm RKKY metal.

• 3d’s. High Tc. Nodal antinodal dichotomy, novel type of Mott transition. Two gap scenario in SC state ?

Thanks!!

Finite T, DMFT and the Energy Landscape of Correlated Materials

T

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

DMFT qp bands

LDA bands LDA bands DMFT qp bands

Quasiparticle bands

three bands, Zj=5/2~1/200

Momentum resolved total spectratrA(,k)

Fujimori, 2003

LDA+DMFT at 10K ARPES, HE I, 15K

LDA f-bands [-0.5eV, 0.8eV] almostdisappear, only In-p bands remain

Most of weight transferred intothe UHB

Very heavy qp at Ef,hard to see in total spectra

Below -0.5eV: almost rigid downshift

Unlike in LDA+U, no new band at -2.5eV

Short lifetime of HBs -> similar to LDA(f-core)rather than LDA or LDA+U

Very slow crossover!

T*

Slow crossover more consistent with NP&F

T*

cohere

nt

spect

ral

weig

ht

T

NP&F: Nakatsuji,Pines&Fisk, 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

Perturbative cluster solver other systems.

Fermi Arcs and Pockets=0.09

Arcs FS in underdoped regimepockets+lines of zeros of G == arcs

Arcs shrink with T!

Curie-Weiss

Tc

Photoemission of Actinidesalpa->delta volume collapse transition

Curium has large magnetic moment and orders antifPu does is non magnetic.

F0=4,F2=6.1

F0=4.5,F2=7.15

F0=4.5,F2=8.11

Gaps of semiconductors

Anomalous Resistivity

2 ( )F Fe k k l

h

Maximum metallic resistivity 2

Fe k

h

Total Energy as a function of volume for Total Energy as a function of volume for Pu Pu (ev) vs (a.u. 27.2 ev)

(Savrasov, Kotliar, Abrahams, Nature ( 2001)Non magnetic correlated state of fcc Pu.

iw

Zein (2005) Following Aryasetiwan Imada Georges Kotliar Bierman and

Lichtenstein. PRB 70 195104. (2004)

Pu

Photoemission Spectra[ Shim. Haule,GK Nature (2007)]

alpa->delta volume collapse transition

F0=4,F2=6.1

F0=4.5,F2=7.15

2020

<l.s> in the late actinides [DMFT results: K. Haule and J. Shim ]

Double well structure and Pu Qualitative explanation of negative thermal expansion[Lawson, A. C., Roberts J. A., Martinez, B., and Richardson, J. W., Jr. Phil. Mag. B, 82, 1837,(2002). G. Kotliar J.Low Temp. Physvol.126, 1009 27. (2002)]

Natural consequence of the conclusions on the model Hamiltonian level. We had two solutions at the same U, one metallic and one insulating. Relaxing the

volume expands the insulator and contract the metal.

F(T,V)=Fphonons+Finvar

What is the range of the correlation self energy (ev) ?

Ce

In

Ir

CeIn

In

Crystal structure of 115’s CeMIn5 M=Co, Ir, Rh

CeIn3 layer

IrIn2 layer

IrIn2 layer

Tetragonal crystal structure

4 in plane In neighbors

8 out of plane in neighbors

3.27au

3.3 au

Fs .7 sc.9 expt 1.17expt bandwidth: 12.6