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Dynamical Mean Field Theory (DMFT) Approach to Correlated Materials

Dynamical Mean Field Theory (DMFT) Approach to Correlated Materials. G. Kotliar Physics Department and Center for Materials Theory Rutgers. Outline. Introduction to the Dynamical Mean Field ideas and techniques. Learning about materials with DMFT: (or Mott physics is everywhere ).

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Dynamical Mean Field Theory (DMFT) Approach to Correlated Materials

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  1. Dynamical Mean Field Theory (DMFT) Approach to Correlated Materials G. Kotliar Physics Department and Center for Materials Theory Rutgers

  2. Outline • Introduction to the Dynamical Mean Field ideas and techniques. • Learning about materials with DMFT: (or Mott physics is everywhere ). • Kappa organics <sp> • The Mott transition across the actinide series , Pu- Am <5f> • Ti2O3 -----LixCoO3----Fe-Ni <3d> • Ce < 4f>

  3. Schematic DMFT phase diagram and DOS of a partially frustrated integer filled Hubbard model and pressure driven Mott transition. Physics Today Vol 57, 53 (2004)

  4. Outline, Collaborators, References • Introduction to extensions of DMFT for applications to electronic structure. [ S. Savrasov and Phys. Rev. B 69, 245101 (2004) ] • C-DMFTstudy of the Mott transition in kappa organics. [O. Parcollet G. Biroli and GK PRL, 92, 226402. (2004) ] • The Mott transition in Actinides Pu [Xi Dai S. Savrasov GK A Migliori H. Ledbetter E. Abrahams Science 300, 953 (2003)] and Am[J. C Griveaux J. Rebizant G. Lander and GK ][Sahana Murthy Ph. D].

  5. MIT in Ti2O3[S. Poteryaev S. Lichtenstein and GK cond-mat 0311319 ] • Alpha Gamma transition in Cerium. K. Haule S. Savrasov V. Udovenko and GK cond-matt 2004.

  6. Weakly correlated electrons. FLT and DFT, and what goes wrong in correlated materials. • Fermi Liquid . . Correspondence between a system of non interacting particles and the full Hamiltonian. • A band structure is generated (Kohn Sham system).and in many systems this is a good starting point for perturbative computations of the spectra (GW).

  7. A different paradigm: the area of influence of a quantum critical point

  8. Energy Landscape of a Correlated Material and a top to bottom approach to correlated materials. Energy T Configurational Coordinate in the space of Hamiltonians

  9. DMFT Cavity Construction: A. Georges and G. Kotliar PRB 45, 6479 (1992). Figure from : G. Kotliar and D. Vollhardt Physics Today 57,(2004)http://www.physics.rutgers.edu/~kotliar/RI_gen.html The self consistent impurity model is a new reference system, to describe strongly correlated materials.

  10. Dynamical Mean Field Theory (DMFT) Cavity Construction: A. Georges and G. Kotliar PRB 45, 6479 (1992).

  11. EDMFT [H. Kajueter Rutgers Ph.D Thesis 1995 Si and Smith PRL77, 3391(1996) R. Chitra and G. Kotliar PRL84,3678 (2000)]

  12. Site Cell. Cellular DMFT. C-DMFT. G. Kotliar,S.. Savrasov, G. Palsson and G. Biroli, Phys. Rev. Lett. 87, 186401 (2001) tˆ(K) hopping expressed in the superlattice notations. • Other cluster extensions (DCA Jarrell Krishnamurthy, Katsnelson and Lichtenstein periodized scheme, Nested Cluster Schemes Schiller Ingersent ), causality issues, O. Parcollet, G. Biroli and GK cond-matt 0307587 (2003)

  13. Two paths for ab-initio calculation of electronic structure of strongly correlated materials Crystal structure +Atomic positions Model Hamiltonian Correlation Functions Total Energies etc. DMFT ideas can be used in both cases.

  14. LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). A Lichtenstein and M. Katsnelson PRB 57, 6884 (1988). • The light, SP (or SPD) electrons are extended, well described by LDA .The heavy, D (or F) electrons are localized treat by DMFT. • LDA Kohn Sham Hamiltonian already contains an average interaction of the heavy electrons, subtract this out by shifting the heavy level (double counting term) • Kinetic energy is provided by the Kohn Sham Hamiltonian (sometimes after downfolding ). The U matrix can be estimated from first principles of viewed as parameters. Solve resulting model using DMFT.

  15. Functional formulation. Chitra and Kotliar (2001), Savrasov and Kotliarcond- matt0308053 (2003). Ir>=|R, r> Double loop in Gloc and Wloc

  16. Next Step: GW+EDMFT S. Savrasov and GK.(2001). in New Theoretical Approaches to Strongly Correlated Systems, A.M. Tsvelik Ed., Kluwer Academic Publishers 259-301, (2001)) W W .P Sun and G. KotliarPhys. Rev. B 66, 85120 (2002)Phys. Rev. Lett. 91, 037209 (2003)Biermann et.al. PRL 90,086402 (2003)

  17. Impurity model representability of spectral density functional.

  18. LDA+DMFT Self-Consistency loop. S. Savrasov and G. Kotliar (2001) and cond-matt 0308053 E U DMFT

  19. Impurity Solvers. • Hubbard I. • Fye Hirsch Quantum Montecarlo. • Interpolative schemes for the self energy. H. Kajueter and G. Kotliar PRL (1996). cond-mat/0401539 V. Oudovenko, K. Haule, S. Savrasov D. Villani and G. Kotliar. • Extensions of NCA. Th. Pruschke and N. Grewe, Z. Phys. B: Condens. Matter 74, 439, 1989. SUNCA K. Haule, S. Kirchner, J. Kroha, and P. W¨olfle, Phys. Rev. B 64, 155111, (2001). K. Haule et. al. (2004)

  20. How good is the local approximation ? • It becomes exact as the coordination number increases or in the limit of infinite dimensions introduced by Metzner and Vollhardt. PRL 62,34, (1989). • How good is it in low dimensions ? Promising recent developments from theory and experiments.

  21. One dimensional Hubbard model .Compare 2 site cluster (in exact diag with Nb=8) vs exact Bethe Anzats,[V. Kancharla C. Bolech and GK PRB 67, 075110 (2003)][ [M. CaponeM.Civelli V Kancharla C.Castellani and GK Phys. Rev. B 69, 195105 (2004)] U/t=4.

  22. Applications of DMFT to materials : Goals of the research • Computations develop a first principles method , based on DMFT, capable of predicting physical properties of correlated materials. • Develop a physical picture of the f and spd electrons in Ce and Pu. • Test the theory against experiments. • Bring theory to the point that it plays an equal role in the field of correlated electron materials. Combining theory and experiment.

  23. Experimental verifications • Finding the QP , the Hubbard band and the transfer of spectral weight between them in optics and photoemission in different materials. • Exploring the various regimes of the phase diagram, including the Mott endpoint using transport probes.

  24. Recent Experiments support qualitative single site DMFT predictions Limelette et. al.(2003) Ito et. al. (1995) Mo et al., Phys. Rev.Lett. 90, 186403 (2003).

  25. Outline • Introduction to the Dynamical Mean Field ideas and techniques. • Learning about materials with DMFT: (or Mott physics is everywhere ). • Kappa organics <sp> • The Mott transition across the actinide series , Pu- Am <5f> • Ti2O3 -----LixCoO3----Fe-Ni <3d> • Ce < 4f>

  26. modeled to triangular lattice t t’ k-(ET)2X are across Mott transition ET = Insulating anion layer X-1 conducting ET layer [(ET)2]+1 Prof. Kanoda U. Tokyo

  27. Mott transition in layered organic conductors S Lefebvre et al. cond-mat/0004455, Phys. Rev. Lett. 85, 5420 (2000)

  28. Theoretical issue: is there a Mott transition in the integer filled Hubbard model, and is it well described by the single site DMFT ?

  29. Double Occupancy vs U • CDMFT Parcollet, Biroli GK PRL (2004) Study frustrated t t’ model t’/t=.9

  30. Evolution of the spectral function at low frequency. If the k dependence of the self energy is weak, we expect to see contour lines corresponding to Ek = const and a height increasing as we approach the Fermi surface.

  31. Evolution of the k resolved Spectral Function at zero frequency. (Parcollet Biroli and GK) U/D=2 U/D=2.25 Uc=2.35+-.05, Tc/D=1/44

  32. Near the transition k dependence is strong. • Qualitative effect, formation of hot regions! • D wave gapping of the single particle spectra as the Mott transition is approached. New paradigm for thinking about the approach to the Mott insulator. • Square symmetry is restored as we approched the insulator. • Experimental predictions! Photoemission ?

  33. Lattice and cluster self energies

  34. Mechanism for hot spot formation: nn self energy ! General phenomena.

  35. Conclusion. • Mott transition survives in the cluster setting. Role of magnetic frustration. • Surprising result: formation of hot and cold regions as a result of an approach to the Mott transition. General result ? • Unexpected role of the next nearest neighbor self energy. • CDMFT a new window to extend DMFT to lower temperatures.

  36. Mott transition in the actinide series (Smith-Kmetko phase diagram)

  37. Total Energy as a function of volume for Pu (Savrasov, Kotliar, Abrahams, 2001,410,793, 2001)

  38. 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)

  39. Mott transition in the actinide series (Smith-Kmetko phase diagram)

  40. Am At room pressure a localised 5f6 system;j=5/2. S = -L = 3: J = 0 J. Smith & R. Haire, Science (1978) J. Smith, J. Phys. (1979)

  41. Mott transition into an open (right) and closed (left) shell systems. S S .5 g T2 Log[2J+1] ??? Uc S=0 U U g ~1/(Uc-U)

  42. Approach the Mott transition, if the localized configuration has an OPEN shell the mass increases as the transition is approached. Consistent theory, entropy increases monotonically as U  Uc . • Approach the Mott transition, if the localized configuration has a CLOSED shell. We have an apparent paradox. To approach the Mott transitions the bands have to narrow, but the insulator has not entropy.. SOLUTION: superconductivity intervenes.

  43. Mott transition in systems with close shell. • Resolution: as the Mott transition is approached from the metallic side, eventually superconductivity intervenes to for a continuous transition to the localized side. • DMFT study of a 2 band model for Buckminster fullerines Capone et. al. Science 2002. • Mechanism is relevant to Americium.

  44. Am under pressure. Lindbaum et.al. PRB 63,2141010(2001)

  45. ITU [J.C. Griveaux J. Rebizant G. Lander]

  46. Overview of rho (p, T) of Am • Note strongly increasing resistivity as f(p) at all T. Shows that more electrons are entering the conduction band • Superconducting at all pressure • IVariation of rho vs. T for increasing p.

  47. DMFT study in the fcc structure. S. Murthy and G. Kotliar fcc

  48. LDA+DMFT spectra. Notice the rapid occupation of the f7/2 band.

  49. One electron spectra. Experiments (Negele) and LDA+DFT theory (S. Murthy and GK )

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