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Dynamical Mean Field Theory of the Mott Transition

Dynamical Mean Field Theory of the Mott Transition. Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University. UBC September 2003.

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Dynamical Mean Field Theory of the Mott Transition

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  1. Dynamical Mean Field Theory of the Mott Transition Gabriel Kotliar Physics Department and Center for Materials Theory Rutgers University UBC September 2003

  2. Abstract: The Mott metal to insulator transition is realized in systems as diverse as the kappa organics, vanadium oxide and nickel selenide nickel sulfide mixtures. We will review the single site DMFT studies as well as a recent cluster DMFT study of this problem (O. Parcollet G. Biroli and G. Kotliar, cond-mat/0308577). We will also review critically recent experiments that test various DMFT predictions in these materials. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  3. Outline • Relevance of the Mott transition problem. • Dynamical Mean Field Theory Single Site and Extensions [I] • Predictions of single site DMFT and observations. • Prediction of cluster DMFT. • Conclusions. • Dynamical Mean Field Theory Single Site and Extensions EDMFT+GW and life without U [II] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  4. The Mott transition problem • Universal and non universal aspects. Frustration. t vs U the fundamental competition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  5. V2O3 under pressure or THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  6. NiSe2-xSx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  7. 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

  8. Pressure Driven Mott transition THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  9. A more general perspective on DMFT. • DMFT as an exact theory. (Chitra and Kotliar PRB 2001 Savrasov and GK cond-matt 2003) • DMFT as an approximation (Chitra and Kotliar PRB2002) • DMFT as a new starting point for perturbative expansions. ( P. Sun and G.K PRB 2002) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  10. DMFT as an exact theory , analogy with DFT Start with TOE THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  11. DFT: effective action construction(Fukuda et.al. ) Chitra and GK THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  12. DFT: Kohn Sham formulation = THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  13. Exchange and correlation energy • Exact formal expressions can be given in terms of a coupling constant integration.[Harris-Jones, adiabatic connection] • DFT is useful because practical accurate expressions for Exc, exist. • LDA, GGA, hybrids, THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  14. Kohn Sham reference system THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  15. Kohn Sham Greens function is an good point to compute spectra in perturbation theory in screenedCoulomb interaction GW,G0W0 Practical implementations, introduce a finite basis set. Division into valence (active ) degrees of freedom and core. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  16. Strongly correlated systems are usually treated with model Hamiltonians THE STATE UNIVERSITY OF NEW JERSEY RUTGERS Conceptually one wants to restrict the number of degrees of freedom by eliminating high energy degrees of freedom. In practice other methods (eg constrained LDA are used)

  17. DMFT • Functional derivation. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  18. DMFT Model Hamiltonian. + Exact functional of the local Greens function A THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  19. DMFT for model Hamiltonians. Kohn Sham formulation. Introduce auxiliary field Exact “local self energy” THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  20. About XC functional. • One can derive a coupling constant integration formulae (Harris Jones formula) for • Generate approximations. • The exact formalism generates the local Greens function and S ii is NOT the self energy. However one can use the approach as starting point for computing other quantities. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  21. Mapping onto impurity models. • The local Greens function A, and the auxilliary quantity S, can be computed from the solution of an impurity model that describes the effects of the rest of the lattice on the on a selected central site. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  22. Comments on functional construction • Atoms as a reference point. Expansion in t. • Locality does not necessarily mean a single point. Extension to clusters. • Jii --- Jii Ji i+d • Aii --- Ai i+d • S ii --- S i i+d • Exact functional G[Aii ,Ai i+d] • The lattice self energy and other non local quantities extending beyond the cluster are OUTSIDE the formalism and need to be inferred. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  23. Comments on funct. construction. • Construction of approximations in the cluster case requires care to maintain causality. • One good approximate construction is the cellular DMFT: a) take a supercell of the desired range,b) • c) obtain estimate of the lattice self energy by restoring translational symmetry. • Many other cluster approximations (eg. DCA, the use of lattice self energy in self consitency condition, restrictions of BK functional, etc. exist). Causality and classical limit of these methods has recently been clarified [ G Biroli O Parcollet and GK] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  24. Lattice and cluster self energies THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  25. DMFT: Cavity Construction THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

  27. Solving the DMFT equations • Wide variety of methods of solution, and they are straighforwardly extended to the cluster setting. • Review: A. Georges, G. Kotliar, W. Krauth and M. Rozenberg Rev. Mod. Phys. 68,13 (1996)] THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  28. Single site DMFT and expt. • Single site DMFT study of the Mott transition, based on a study of the Hubbard model on frustrated lattices made several interesting qualitative predictions. • New experiments and reexamination of old ones give some credence to that the local picture is quite good. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  29. V2O3 under pressure or THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  30. 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

  31. NiSe2-xSx THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  32. Qualitative single site DMFT predictions. • Spectra of the strongly correlated metallic regime contains both quasiparticle-like and Hubbard band-like features. • Mott transition is drive by transfer of spectral weight. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  33. Schematic Phase Diagram of the Frustrated Hubbard model THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

  35. Searching for a quasiparticle peak THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  36. Schematic DMFT phase diagram Hubbard model (partial frustration). Evidence for QP peak in V2O3 from optics. M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  37. 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

  38. QP in V2O3 was recently found Mo et.al THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  39. Different transport regimes. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  40. Anomalous Resistivity and Mott transition Ni Se2-x Sx Crossover from Fermi liquid to bad metal to semiconductor to paramagnetic insulator. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  41. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  42. Phase Diagram k Organics THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  43. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  44. Transport in k organics THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  45. Ising endpoint finally found THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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

  47. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  48. Ising critical endpoint! In V2O3 P. Limelette et.al. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  49. Conclusion. • An electronic model accounts for all the qualitative features of the finite temperature of a frustrated system at integer occupancy. • The observation of the spinodal lines and the wide classical critical region where mean field holds indicate the coupling to the lattice is quantitatively very important. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

  50. Cluster studies of the Mott transition. THE STATE UNIVERSITY OF NEW JERSEY RUTGERS

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