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 (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, (2000) PRB 63, (2001) Ir,>=|R,  > Gloc=G(R , R’  ’ )  R,R’ Introduce Notion of Local Greens functions, Wloc, Gloc G=Gloc+Gnonloc. Electronic structure problem: compute and given structure

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, (1994). Convergence as a function of size. Zein Savrasov and Kotliar PRL 96, (2006) expt-gap 1.17 Theory.9 expt bandwidth: 12.6 theory 13.7

GW self energy for Si Self energy corrections beyond GW Coordination Sphere Locality of correlations Zein Savrasov and GK PRL 96, (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. CeMIn 5 M=Co, Ir, Rh out of plane in-plane Ce In Ir

Angle integrated photoemission Experimental resolution ~30meV Surface sensitivity at 122 ev, theory predicts 3meV broad band Expt Fujimori et al., PRB 73, (2006) P.R B 67, (2003). Theory: LDA+DMFT, impurity solvers SUNCA and CTQMC Shim Haule and GK (2007)

Very slow crossover! T*T* Slow crossover more consistent with NP&F T*T* coherent spectral weight T NP&F: Nakatsuji,Pines&Fisk, 2004 Buildup of coherence in single impurity case TKTK coherent spectral weight T scattering rate coherence peak Buildup of lattice coherence Crossover around 50K

Momentum resolved total spectra trA( ,k) Fujimori, PRB LDA+DMFT at 10K ARPES, HE I, 15K LDA f-bands [-0.5eV, 0.8eV] almost disappear, only In-p bands remain Most of weight transferred into the 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, (2005). 16. K. S. Burch et al., PRB 75, (2007). 17. E. J. Singley, D. N. Basov, E. D. Bauer, M. B. Maple, PRB 65, (R) (2002).

Ce In Multiple hybridization gaps 300K eV 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    Pu  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 (2005). Valence of Pu is controversial.

DMFT Phonons in fcc  -Pu C 11 (GPa) C 44 (GPa) C 12 (GPa) C'(GPa) Theory Experiment ( 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, (2005) Aimi and Imada arXiv:

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 k K.M. Shen et.al X2 CDMFT Nodal Region Antinodal Region Civelli et.al. PRL 95 (2005) Senechal eta. PRL 94 (20050

Nodal Antinodal Dichotomy and pseudogap.

Superconducting Nodal quasiparticles

Antinodal gap M. Civelli, cond-mat G. 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, (2007). Tanaka et. al. Science 315, 1910 (2006) Kanigel et.al. PRL (2007) Photoemission expts ?

Thanks! SP electrons. Zein Savrasov and GK PRL 96, (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 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=300K scattering rate~100meVFingerprint of spd’s due to hybridization Not much weight q.p. bandSO Momentum resolved Ce-4f spectra Af(,k)Af(,k) Hybridization gap

DMFT qp bandsLDA bands DMFT qp bands Quasiparticle bands three bands, Z j=5/2 ~1/200

Momentum resolved total spectra trA( ,k) Fujimori, 2003 LDA+DMFT at 10K ARPES, HE I, 15K LDA f-bands [-0.5eV, 0.8eV] almost disappear, only In-p bands remain Most of weight transferred into the 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*T* Slow crossover more consistent with NP&F T*T* coherent spectral weight T NP&F: Nakatsuji,Pines&Fisk, 2004 Buildup of coherence in single impurity case TKTK coherent spectral weight 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 regime pockets+lines of zeros of G == arcs Arcs shrink with T!

Curie-Weiss Tc Photoemission of Actinides alpa->delta volume collapse transition Curium has large magnetic moment and orders antif Pu 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 Maximum metallic resistivity

Total Energy as a function of volume for Pu Total Energy as a function of volume for Pu  (ev) vs (a.u ev) (Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu. Zein (2005) Following Aryasetiwan Imada Georges Kotliar Bierman and Lichtenstein. PRB (2004) Pu

Photoemission Spectra[ Shim. Haule,GK Nature (2007)] alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=

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. Phys vol.126, (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 Ce In Crystal structure of 115’s CeMIn5 M=Co, Ir, Rh CeIn 3 layer IrIn 2 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 1.17 expt bandwidth: 12.6