Electronic Structure of Strongly Correlated Materials : a DMFT Perspective

1. Electronic Structure of Strongly Correlated Materials : a DMFT Perspective Workshop on Opportunities in Materials Theory October 4-6 2000 Gabriel Kotliar Rutgers University Supported by the NSF -DMR

2. Outline • Introduction to the electronic structure of correlated electrons • Dynamical Mean Field Theory • Delocalization - Localization Transition in frustrated systems:universality at high temperatures • A case study of system specific properties: d Pu (S. Savrasov, supported by DOE, Basic Energy Sciences) • Outlook THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

3. How to think about an electron in a solid ? Standard Model of Solids High densities, electron as a wave, band theory, k-space One particle excitations: quasi-particle bands Au, Cu, Si…… THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

4. Standard Model Odd # electrons -> metal Even # electrons -> insulator • Theoretical foundation: Sommerfeld, Bloch and Landau • Computational tools DFT in LDA • Transport Properties, Boltzman equation , low temperature dependence of transport coefficients Typical Mott values of the resistivity 200 mOhm-cm Residual instabilites SDW, CDW, SC THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

5. Mott : correlations localize the electron Low densities, electron as a particle, atomic physics, real space One particle excitations: Hubbard bands NiO, CoO MnO…. Magnetic and Orbital Ordering at low T Quantitative calculations of Hubbard bands and exchange constants, LDA+ U THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

6. Localization vs Delocalization • A large number of compounds with electrons which are not close to the well understood limits (localized or itinerant). • These systems display anomalous behavior (departure from the standard model of solids). • Neither LDA or LDA+U works well • Dynamical Mean Field Theory: Simplest approach to the electronic structure, which interpolates correctly between atoms and bands THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

7. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

9. Failure of the StandardModel: Anomalous Spectral Weight Transfer Optical Conductivity o of FeSi for T=,20,20,250 200 and 250 K from Schlesinger et.al (1993) Neff depends on T THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

10. Strong Correlation Problem • Large number of f and d electrons based compounds • Hamiltonian is known. Identify the relevant degrees of freedom at a given scale. • Treat the itinerant and localized aspect of the electron • The Mott transition, head on confrontation with this issue • Dynamical Mean Field Theory simplest approach interpolating between that bands and atoms THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

11. Hubbard model • U/t • Doping d or chemical potential • Frustration (t’/t) • T temperature Mott transition as a function of doping, pressure temperature etc. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

12. Two routes to the Mott transition: Bandwidth-Control (“U/D”) and Filling-Control (doping)Imada et.al RMP (1999) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

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

15. Solving the DMFT equations • Wide variety of computational tools (QMC, NRG,ED….) • Analytical Methods THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

16. DMFT: Methods of Solution THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

17. Reviews of DMFT • Prushke T. Jarrell M. and Freericks J. Adv. Phys. 44,187 (1995) • A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

18. DMFT • Spin Orbital Ordered States • Longer range interactions Coulomb, interactions, Random Exchange (Sachdev and Ye, Parcollet and Georges, Kajueter and Kotliar, Si and Smith, Chitra and Kotliar,) • Short range magnetic correlations. Cluster Schemes. (Ingersent and Schiller, Georges and Kotliar, cluster expansion in real space, momentum space cluster DCA Jarrell et.al. ). THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

19. DMFT • Formulation as an electronic structure method (Chitra and Kotliar) • Density vs Local Spectral Function • Extensions to treat strong spatial inhomogeneities. Anderson Localization (Dobrosavlevic and Kotliar),Surfaces (Nolting),Stripes (Fleck Lichtenstein and Oles) • Practical Implementation (Anisimov and Kotliar, Savrasov, Katsenelson and Lichtenstein) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

20. Insights from DMFT • Low temperatures several competing phases . Their relative stability depends on chemistry and crystal structure • High temperature behavior around Mott endpoint, more universal regime, captured by simple models treated within DMFT THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

21. Schematic DMFT phase diagram Hubbard model (partial frustration) Rozenberg et.al. PRL (1995) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

22. Kuwamoto Honig and AppellPRB (1980) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

23. A time-honored example: Mott transition in V2O3 under pressure or chemical substitution on V-site THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

25. 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

26. Evolution of the Spectral Function with Temperature Anomalous transfer of spectral weight connected to the proximity to the Mott endpoint (Kotliar Lange and Rozenberg 2000) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

27. Ising character of the transfer of spectral weight Ising –like dependence of the photo-emission intensity and the optical spectral weight near the Mott transition endpoint THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

28. ARPES measurements on NiS2-xSexMatsuura et. Al Phys. Rev B 58 (1998) 3690 . THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

29. Spectral Evolution at T=0 half filling full frustration X.Zhang M. Rozenberg G. Kotliar (PRL 1993) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

30. Parallel development: Fujimori et.al THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

31. Anomalous Resistivities and Mott phenomena (Rozenberg et. al 1995) Resistivity exceeds the Mott limit THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

32. Anomalous Resistivity and Mott transition Ni Se2-x Sx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

33. 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 THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

34. Landau Functional G. Kotliar EPJB (1999) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

35. 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 • Hubbard bands and QP bands • The puzzle of elemental plutonium (S. Savrasov) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

36. Delocalization Localization Transition across the actinide series THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

37. Problems with LDA • DFT in the LDA or GGA is a well established tool for the calculation of ground state properties. • Many studies (Freeman, Koelling 1972, ….Beottger et.al 1998, Wills et.al. 1999) give • an equilibrium volume of the d phaseIs 35% lower than experiment • This is the largest discrepancy ever known in DFT based calculations. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

38. Pu: Complex Phase Diagram (J. Smith LANL) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

39. Anomalous ResistivityJ. Smith LANL THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

40. Pu Specific Heat THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

41. Pu: DMFT total energy vs Volume (Savrasov 00) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

42. Pu Spectra DMFT(Savrasov) EXP (Arko et. Al) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

43. S. Savrasov: DMFT Lab THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

44. Strongly Correlated Electrons • Competing Interaction • Low T, Several Phases Close in Energy • Complex Phase Diagrams • Extreme Sensitivity to Changes in External Parameters • Need for Realistic Treatments THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

45. Outlook • Strongly correlated electron exhibit unusual characteristics, complex systems. • Two recent examples: large Thermoelectric response in CeFe4 P12 (H. Sato et al. cond-mat 0010017). Large Ultrafast Optical Nonlinearities Sr2CuO3 (T Ogasawara et.al cond-mat 000286) • Theory will play an important role in optimizing their physical properties. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

46. Outlook • The Strong Correlation Problem:How to deal with a multiplicity of competing low temperature phases and infrared trajectories which diverge in the IR • Strategy: advancing our understanding scale by scale • Generalized cluster methods to capture longer range magnetic correlations • New structures in k space? THE STATE UNIVERSITY OF NEW JERSEY RUTGERS