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Electronic Structure of Correlated Materials : a DMFT Perspective

Electronic Structure of Correlated Materials : a DMFT Perspective. Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University and KITP Institute for Theoretical Physics UCSB Santa Barbara. Brookhaven National Laboratory September 12 th 2002.

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Electronic Structure of Correlated Materials : a DMFT Perspective

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  1. Electronic Structure of Correlated Materials : a DMFT Perspective Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University and KITP Institute for Theoretical Physics UCSB Santa Barbara Brookhaven National Laboratory September 12th 2002 Supported by the NSF DMR 0096462

  2. Outline • The Mott transition problem and electronic structure. • Dynamical Mean Field Theory • Model Hamiltonian Studies of the Mott transition. Universal aspects. • System specific studies of materials. LDA+DMFT. Some case studies. • Outlook THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  3. Weakly correlated electrons:band theory. • Simple conceptual picture of the ground state, excitation spectra, transport properties of many systems (simple metals, semiconductors,….). • A methods for performing quantitative calculations. (Density functional theory, in various approximations). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  4. The electron in a solid: wave picture Momentum Space (Sommerfeld) Maximum metallic resistivity 200 mohm cm Standard model of solids (Bloch, Landau) Periodic potential, waves form bands , k in Brillouin zone . Interactions renormalize away. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  5. Standard Model of Solids • Qualitative predictions: low temperature dependence of thermodynamics and transport. • Optical response, transition between the bands. • Qualitative predictions: filled bands give rise to insulting behavior. Compounds with odd number of electrons are metals. • Quantitative tools: Density Functional Theory with approximations suggested by the Kohn Sham formulation, (LDA GGA) is a successful computational tool for the total energy. Good starting point for perturbative calculation of spectra,eg. GW. Kinetic equations yield transport coefficients. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  6. Kohn Sham reference system Excellent starting point for computation of spectra in perturbation theory in screened Coulomb interaction GW. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  7. Success story : Density Functional Linear Response Tremendous progress in ab initio modelling of lattice dynamics & electron-phonon interactions has been achieved (Review: Baroni et.al, Rev. Mod. Phys, 73, 515, 2001) (Savrasov, PRB 1996)

  8. The electron in a solid: particle picture. • Array of hydrogen atoms is insulating if a>>aB. Mott: correlations localize the electron e_ e_ e_ e_ • Superexchange Think in real space , solid collection of atoms High T : local moments, Low T spin-orbital order THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  9. Mott : Correlations localize the electron Low densities, electron behaves as a particle,use atomic physics, real space One particle excitations: Hubbard Atoms: sharp excitation lines corresponding to adding or removing electrons. In solids they broaden by their incoherent motion, Hubbard bands (eg. bandsNiO, CoO MnO….) H H H+ H H H motion of H+ forms the lower Hubbard band H H H H- H H motion of H_ forms the upper Hubbard band Quantitative calculations of Hubbard bands and exchange constants, LDA+ U, Hartree Fock. Atomic Physics. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  10. Photoemission spectroscopy. Measures density of states for (BIS)adding and (PES) removing electrons THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  11. Localization vs Delocalization Strong Correlation Problem • A large number of compounds with electrons in partially filled shells, are not close to the well understood limits (localized or itinerant). Non perturbative problem. • These systems display anomalous behavior (departure from the standard model of solids). • Neither LDA or LDA+U or Hartree Fock work well. • Dynamical Mean Field Theory: Simplest approach to electronic structure, which interpolates correctly between atoms and bands. Treats QP bands and Hubbard bands. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  12. Strong correlation anomalies • Metals with resistivities which exceed the Mott Ioffe Reggel limit. • Transfer of spectral weight which is non local in frequency. • Dramatic failure of DFT based approximations in predicting physical properties. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  13. Correlated Materials do big things • Huge resistivity changes V2O3. • Copper Oxides. .(La2-x Bax) CuO4 High Temperature Superconductivity.150 K in the Ca2Ba2Cu3HgO8 . • Uranium and Cerium Based Compounds. Heavy Fermion Systems,CeCu6,m*/m=1000 • (La1-xSrx)MnO3 Colossal Magneto-resistance. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  14. Strongly Correlated Materials. • Large thermoelectric response in CeFe4 P12 (H. Sato et al. cond-mat 0010017). Ando et.al. NaCo2-xCuxO4 Phys. Rev. B 60, 10580 (1999). • Large and ultrafast optical nonlinearities Sr2CuO3 (T Ogasawara et.a Phys. Rev. Lett. 85, 2204 (2000) ) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  15. Mott transition in V2O3 under pressure or chemical substitution on V-site THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  16. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  17. Failure of the Standard Model: NiSe2-xSx Miyasaka and Takagi (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  18. Mean-Field : Classical vs Quantum Classical case Quantum case A. Georges, G. Kotliar (1992) Phys. Rev. B 45, 6497 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  19. Limit of large lattice coordination Metzner Vollhardt, 89 Muller-Hartmann 89 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  20. DMFT Impurity cavity construction THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  21. E-DMFT references • H. Kajueter and G. Kotliar (unpublished and Kajuter’s Ph.D thesis). • Q. Si and Smith PRL [analysis of quantum critical points] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  22. C-DMFT: test in one dimension. (Bolech, Kancharla GK cond-mat 2002) Gap vs U, Exact solution Lieb and Wu, Ovshinikov Nc=2 CDMFT vs Nc=1 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  23. Insights from DMFT • Low temperature Ordered phases . Stability depends on chemistry and crystal structure • High temperature behavior around Mott endpoint, more universal regime, captured by simple models treated within DMFT. Role of magnetic frustration. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  24. Schematic DMFT phase diagram Hubbard model (partial frustration) M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkikne J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  25. Kuwamoto Honig and Appell PRB (1980)M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkikne J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  26. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  27. Phase Diag: Ni Se2-x Sx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  28. Insights from DMFT • The Mott transition is driven by transfer of spectral weight from low to high energy as we approach the localized phase • Control parameters: doping, temperature,pressure… THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  29. Evolution of the Spectral Function with Temperature Anomalous transfer of spectral weight connected to the proximity to the Ising Mott endpoint (Kotliar Lange and Rozenberg Phys. Rev. Lett. 84, 5180 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  30. ARPES measurements on NiS2-xSexMatsuura et. al Phys. Rev B 58 (1998) 3690. Doniach and Watanabe Phys. Rev. B 57, 3829 (1998) . THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  31. Mott transition in V2O3 under pressure or chemical substitution on V-site THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  32. Anomalous transfer of optical spectral weight V2O3 :M Rozenberg G. Kotliar and H. Kajuter Phys. Rev. B 54, 8452 (1996). M. Rozenberg G. Kotliar H. Kajueter G Tahomas D. Rapkikne J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  33. Anomalous Spectral Weight Transfer: Optics Below energy ApreciableT dependence found. Schlesinger et.al (FeSi) PRL 71 ,1748 , (1993) B Bucher et.al. Ce2Bi4Pt3PRL 72, 522 (1994), Rozenberg et.al. PRB 54, 8452, (1996). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  34. ARPES measurements on NiS2-xSexMatsuura et. Al Phys. Rev B 58 (1998) 3690. Doniaach and Watanabe Phys. Rev. B 57, 3829 (1998) . THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  35. Anomalous transfer of optical spectral weight, NiSeS. [Miyasaka and Takagi] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  36. Anomalous Resistivity and Mott transition Ni Se2-x Sx Insights from DMFT: think in term of spectral functions (branch cuts) instead of well defined QP (poles ) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  37. Qualitative phase diagram in the U, T , m plane (two band Kotliar Murthy Rozenberg PRL (2002). • Coexistence regions between localized and delocalized spectral functions. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  38. QMC calculationof n vs m (Kotliar Murthy Rozenberg PRL 2002, 2 band, U=3.0) k diverges at generic Mott endpoints THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  39. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  40. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  41. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  42. Insights from DMFT • Mott transition as a bifurcation of an effective action • Important role of the incoherent part of the spectral function at finite temperature • Physics is governed by the transfer of spectral weight from the coherent to the incoherent part of the spectra. Real and momentum space. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  43. Two roads for ab-initio calculation of electronic structure of strongly correlated materials Crystal structure +Atomic positions Model Hamiltonian Correlation Functions Total Energies etc. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  44. Realistic Calculationsof the Electronic Structure of Correlated materials • Combinining DMFT with state of the art electronic structure methods to construct a first principles framework to describe complex materials. • Anisimov Poteryaev Korotin Anhokin and Kotliar J. Phys. Cond. Mat. 35, 7359 (1997) • Savrasov Kotliar and Abrahams Nature 410, 793 (2001)) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  45. Combining LDA and DMFT • The light, SP (or SPD) electrons are extended, well described by LDA • The heavy, D (or F) electrons are localized,treat by DMFT. • LDA already contains an average interaction of the heavy electrons, subtract this out by shifting the heavy level (double counting term) The U matrix can be estimated from first principles or viewed as parameters THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  46. Materials…… • Pu • Fe, Ni, • La1-x Srx TiO3 • NiO • ……………. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  47. Case study in f electrons, Mott transition in the actinide series. B. Johanssen 1974 Smith and Kmetko Phase Diagram 1984. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  48. Problems with density functional treatements of d Pu DFT in the LDA or GGA is a well established tool for the calculation of ground state properties. Many studies (APW Freeman, Koelling 1972, ASA and FP-LMTO, Soderlind et. al 1990, Kollar et.al 1997, Boettger et.al 1998, Wills et.al. 1999) show an equilibrium volume of the d phaseIs 35% lower than experiment This is the largest discrepancy ever known in DFT based calculations. LSDA predicts magnetic long range order which is not observed experimentally (Solovyev et.al.) If one treats the f electrons as part of the core LDA overestimates the volume by 30% Weak correlation picture for alpha phase.

  49. Pu DMFT total energy vs Volume (Savrasov Kotliar and Abrahams Nature 410, 793 (2001) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  50. Lda vs Exp Spectra (Joyce et.al.) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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