**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. COE 21 Workshop Applied Physics on Strong Correlation September 27-29 (2007) Tokyo Japan

**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

**Electronic structure problem: compute <r|G|r’> and** <r|W|r’> given structure Chitra and Kotliar PRB 62, 12715 (2000) PRB 63, 115110 (2001) Introduce Notion of Local Greens functions, Wloc, Gloc G=Gloc+Gnonloc . Ir,>=|R, r,> Gloc=G(R r, R’ r’) dR,R’

**“ Local” can mean a small cluster of sites or multiple** unit cells. Cellular DMFT, cluster DMFT. DMFT mapping: site or cluster of sites in a self consistent medium. Quantum impurity solver, gives S and P. Approximate the self energy of a subset “ uncorrelated electrons “ by the LDA Vxc(r)d(r,r’) replace W(w) by a static U acting only the “correlated “ set, treated by DMFT. 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)

**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. expt-gap 1.17 Theory .9expt bandwidth: 12.6 theory 13.7 Zein Savrasov and Kotliar PRL 96, 226403 (2006)

**Locality of correlations Zein Savrasov and GK PRL 96,** 226403 (2006)) Self energy corrections beyond GW GW self energy for Si Coordination Sphere Coordination Sphere Similar conclusion for other materials, Na, Al, Fe Ni……..

**Ir** In Ce CeRhIn5: TN=3.8 K; 450 mJ/molK2CeCoIn5: 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

**Angle integrated photoemission ** Expt Fujimori et al., PRB 73, 224517 (2006) P.R B 67, 144507 (2003). Experimental resolution ~30meV Surface sensitivity at 122 ev , theory predicts 3meV broad band Theory: LDA+DMFT, impurity solvers SUNCA and CTQMC Shim Haule and GK (2007)

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

**Momentum resolved total spectra** trA(w,k) Most of weight transferred into the UHB LDA f-bands [-0.5eV, 0.8eV] almost disappear, only In-p bands remain 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 ARPES, HE I, 15K LDA+DMFT at 10K Fujimori, PRB Short lifetime of HBs -> similar to LDA(f-core) rather than LDA or LDA+U

**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). • 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

**10K** In eV Ce In Multiple hybridization gaps non-f spectra 300K • Larger gap due to hybridization with out of plane In • Smaller gap due to hybridization with in-plane In

**Mott transition across the actinides. B. Johansson Phil Mag.** 30,469 (1974)] Mott Transition d Pu a d a after G. Lander, Science (2003) and Lashley et. al. PRB (2006).

**Pu phases: A. Lawson Los Alamos Science 26, (2000) ** GGA LSDA predicts d Pu to be magnetic with a large moment ( ~5 Bohr). Experimentally Pu is not magnetic. [PRB 054416(2005). Valence of Pu is controversial.

** 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 DMFT Phonons in fcc d-Pu ( 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** Doping driven Mott transition in 2d-single band spin 1/2 system. Does a plaquette DMFT of simple model Hamiltonians, (Hubbard and t-J) , capture the qualitative physics of cuprates ? 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 k 2X2 CDMFT K.M. Shen et.al. 2004 Antinodal Region Civelli et.al. PRL 95 (2005) Senechal eta. PRL 94 (20050 Nodal Region

**Nodal Antinodal Dichotomy and pseudogap.**

** Superconducting Nodal quasiparticles**

**M. Civelli, cond-mat 0704.1486** G. Kotliar and K Haule PRB (2007) Normal self energy contribution monotonically decreasing Anomalous self energy contribution has a dome like shape (like vD) Antinodal gap Photoemission expts ? Kondo Takeuchi Kaminski Tsuda and shin, PRL 98, 267004 (2007). Tanaka et. al. Science 315 , 1910 (2006) Kanigel et.al. PRL (2007)

**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

**Momentum resolved Ce-4f spectra** Af(w,k) Hybridization gap q.p. band Fingerprint of spd’s due to hybridization scattering rate~100meV SO Not much weight T=10K T=300K

**DMFT qp bands** LDA bands LDA bands DMFT qp bands Quasiparticle bands three bands, Zj=5/2~1/200

**Momentum resolved total spectra** trA(w,k) Most of weight transferred into the UHB LDA f-bands [-0.5eV, 0.8eV] almost disappear, only In-p bands remain 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 ARPES, HE I, 15K LDA+DMFT at 10K Fujimori, 2003 Short lifetime of HBs -> similar to LDA(f-core) rather than LDA or LDA+U

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

** Perturbative cluster solver other systems. **

**Fermi Arcs and Pockets** d=0.09 Arcs FS in underdoped regime pockets+lines ofzeros of G == arcs Arcs shrink with T!

**Curie-Weiss** Tc Photoemission of Actinides alpa->delta volume collapse transition F0=4,F2=6.1 F0=4.5,F2=7.15 F0=4.5,F2=8.11 Curium has large magnetic moment and orders antif Pu does is non magnetic.

**Gaps of semiconductors**

**Anomalous Resistivity** Maximum metallic resistivity

**Total Energy as a function of volume for Pu W(ev) vs ** (a.u. 27.2 ev) Pu Zein (2005) Following Aryasetiwan Imada Georges Kotliar Bierman and Lichtenstein. PRB 70 195104. (2004) (Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu.

**Photoemission Spectra[ Shim. Haule,GK Nature (2007)]** alpa->delta volume collapse transition F0=4.5,F2=7.15 20 F0=4,F2=6.1

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

**Double well structure and d 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)] F(T,V)=Fphonons+Finvar 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.

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

**Ir** In Ce In Ce In Crystal structure of 115’s CeMIn5 M=Co, Ir, Rh Tetragonal crystal structure IrIn2 layer 3.27au 4 in plane In neighbors 3.3 au CeIn3 layer IrIn2 layer 8 out of plane in neighbors

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