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Towards a Realistic DMFT based Theoretical Transport and Spectroscopy of Correlated Solids

Towards a Realistic DMFT based Theoretical Transport and Spectroscopy of Correlated Solids. G.Kotliar Physics Department Center for Materials Theory Rutgers University. CRISMAT Caen October 30 (2007). Outline.

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Towards a Realistic DMFT based Theoretical Transport and Spectroscopy of Correlated Solids

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  1. Towards a Realistic DMFT based Theoretical Transport and Spectroscopy of Correlated Solids G.Kotliar Physics Department Center for Materials Theory Rutgers University. CRISMAT Caen October 30 (2007)

  2. Outline • 1]Introduction to correlated electrons and DMFT ideas. Central theme, localization-delocalization ! Thermoelectricity. • 2] d’s Doped Titanites. Doping driven Mott transition.[G. Kotliar and G. Palsson PRLPRL 80, (1998), 4775] • 3] 4f’s 115’s and the tale of multiple hybridization gaps.[K. Haule J. Shim G. Kotliar, Science Nov 1st 2007] • 4] Conclusions

  3. Correlated Electron Systems Pose Basic Questions in CMT • FROM ATOMS TO SOLIDS • How to describe electron from localized to itinerant ? • How do the physical properties evolve ?

  4. DMFT Spectral Function Photoemission and correlations e • Probability of removing an electron and transfering energy w=Ei-Ef, and momentum k f(w) A(w, K) M2 n n Angle integrated spectral function 8

  5. Georges Kotliar (1992)DMFT approximate quantum solid as atom in a medium 10

  6. Spectra=- Im G(k,w) Self consistency for V and e (GW) DFT+DMFT: determine H[k] and density and S self consitently from a functional and obtain total energies. 12

  7. Electronic structure problem: compute <r|G|r’> and <r|W|r’> given structure Chitra and Kotliar PRB 62, 12715 (2000) PRB (2001)P.Sun and GK (2005) Zein et.al.PRL 96, 226403 (2006)). See also Bierman Aryasetiwan and Georges. Introduce Notion of Local Greens functions, Wloc, Gloc G=Gloc+Gnonloc . Ir,>=|R, r,> Gloc=G(R r, R’ r’) dR,R’

  8. “ 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 model, gives S and P.Need accurate impurity solvers.. Approximate the self energy of a subset “ uncorrelated electrons “ by dft Vxc(r)d(r,r’) replace W(w) by a static U acting only on the “correlated “ set, which we treat 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)

  9. Summary: part 1 Spectral function in DMFT analogous to density in DFT Self consistent Impurity problem, natural language to describe localization/delocalization phenomena. combines atomic physics and band theory Systematically improvable, cluster DMFT Recent progress in implementation • Gabriel Kotliar and Dieter Vollhardt, Physics Today 57, 53 (2004). • A. Georges, G. Kotliar, W. Krauth, and M. Rozenberg, Rev. of Mod. Phys. 68, 13-125 (1996). • G. Kotliar, S. Savrasov, K. Haule, V. Oudovenko, O. Parcollet, and C. Marianetti, Rev. of Mod. Phys. 78, 000865 (2006).

  10. Thermoelectric Figure of Merit • ZT = T S2 /kr k = kel + kLattice Best Case, Suppose kLattice = 0 ZT = T S2 /kel r • Wiedemann-Franz law • L0 = kel r/T= 2.4 x 10-8 V2/K2 • or ZT = S2/ L0 • which means that for ZT=1, • or S > 156 mV/K Basic Scale k/e 86 10-6 V /K

  11. “Best” Thermoelectrics Among Mixed Valence Intermetallics(Physics Today, March 1997) G. Mahan B. Sales J. Sharp

  12. “State-of-the-art” Thermoelectric Materials. MRS Talk 2004 B. Sales ONRL

  13. Outline • 1]Introduction to correlated electrons and DMFT ideas. Central theme, localization-delocalization ! Thermoelectricity. • 2]d’s Doped Titanites. Doping driven Mott transition. • 3] 4f’s 115’s and the tale of multiple hybridization gaps. • 4] Conclusions

  14. (Tokura et. al. PRL 1993)A doped Mott insulator:La1-ySryO3 La+++ Ti+++ (O3)-- Mott insulator . (3d)1 one electron per site. x holes y electrons.

  15. DMFT calculation U near the Mott transition, M. Rozenberg Zhang and GK PRB (1994)DMFT black dots.

  16. Hall Coefficient: expt. Tokura(1993) Theory Kajueter PRB (1996)

  17. LaSrTiO3 photoemission Fujimori et.al.expt. Theory Kajuter and GK

  18. Low T Fermi Liquid DMFT analysis in limiting cases. Palsson and GK PRL (1998) High T Localized “ particle-like” regime

  19. Theory : Palsson and Kotliar PRL 80, (1998), 4775 Expt. C.C. Hays PRB 90 (1999),10367

  20. PRB (2001) Theory ? DD Sarma Barman Kajueter Kotliar EPL (1996 ) Even more spectacular, electron gas on SrTiO3 interface. Nature (2007)

  21. Outline • 1]Introduction to correlated electrons and DMFT ideas. Central theme, localization-delocalization ! Thermoelectricity. • 2] d’s Doped Titanites. Doping driven Mott transition. • 3] 4f’s 115’s and the tale of multiple hybridization gaps. • 4] Conclusions

  22. Ir In Ce  CeRhIn5: TN=3.8 K;   450 mJ/molK2CeCoIn5: Tc=2.3 K;   1000 mJ/molK2; CeIrIn5: Tc=0.4 K;   750 mJ/molK2 CeMIn5 M=Co, Ir, Rh out of plane in-plane

  23. 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

  24. 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

  25. 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)

  26. 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

  27. w k first mid-IR peak at 250 cm-1 CeCoIn5 Optical conductivity F.P. Mena & D.Van der Marel, 2005 Typical heavy fermion at low T: no visible Drude peak no sharp hybridization gap Narrow Drude peak (narrow q.p. band) Hybridization gap second mid IR peak at 600 cm-1 Interband transitions across hybridization gap -> mid IR peak E.J. Singley & D.N Basov, 2002

  28. 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

  29. 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

  30. 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

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

  32. Summary • 115’s model systems to study the evolution of the f electron as a function of temperature • Multiple hybridization gaps in optics. • Very different Ce-In hybridizations with In out of plane being larger. J. Shim K Haule and G.K Science Express November 1st (2007).

  33. Outline • 1]Introduction to correlated electrons and DMFT ideas. Central theme, localization-delocalization ! Thermoelectricity. • 2] d’s Doped Titanites. Doping driven Mott transition. • 3] 4f’s 115’s and the tale of multiple hybridization gaps. • 4] Conclusions

  34. Conclusion • Strongly Correlated electrons, still fertile ground for discovery of new thermoelectrics. • Theory has improved, DMFT! can it play now some role in assisting and guiding experimental discoveries ?

  35. Na0.7CoO2 (Terasaki). Good oxide thermoelectric K. Fujita et al. Jpn. J. Appl. Phys. 40 (2001) 4644

  36. DMFT study of Nax CoO2

  37. Foo et.al. PRL 247001

  38. CoO2 NaCoO2

  39. Theoretical Issues: Na-Induced Correlations in NaxCoO2 C. A. Marianetti and G. Kotliar Phys. Rev. Lett. 98, 176405 (2007) • What is the minimal model of the cobaltes ? • t2g orbitals + binary potential a see which results of the Li /Na vacancy . • Why are correlations stronger near a band insulator than near a Mott insulator ? • U < Uc2 , hole moves in a restricted space (where potential is low) and is strongly correlated. • DMFT calculations account for the Curie Weiss phase and the Fermi liquid phase

  40. Assume Na patterns of Zandbergen et. al.PRB 70 024101 C. A. Marianetti and G. Kotliar Phys. Rev. Lett. 98, 176405 (2007) . A

  41. DMFT calculations with and without disorder U=3 ev. C. A. Marianetti and G. Kotliar Phys. Rev. Lett. 98, 176405 (2007)

  42. x=.33 QP dispersion LDA+DMFTC. Marianetti K. Haule and O Parcollet to appear in PRL

  43. FeSb2 Bentien et. al.

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