Strongly correlated materials from Dynamical Mean Field Perspective.

1. Strongly correlated materials from Dynamical Mean Field Perspective. Thanks to:G.Kotliar, S. Savrasov, V. Oudovenko DMFT(SUNCA method) two-band Hubbard model Bethe lattice, U=4D

2. Overview • Application of DMFT to real materials (LDA+DMFT) • Extensions of DMFT to clusters and its application to models for high-Tc

3. mapping fermionic bath Dynamical Mean Field Theory Basic idea of DMFT: reduce the quantum many body problem to a one site or a cluster of sites, in a medium of non interacting electrons obeying a self consistency condition. Basic idea of Spectral density functional approach: instead of using functionals of the density, use more sensitive functionals of the one electron spectral function. [density of states for adding or removing particles in a solid, measured in photoemission]

4. Coherence incoherence crossover in a model Phase diagram of a Hubbard model with partial frustration at integer filling.  M. Rozenberg et.al., Phys. Rev. Lett. 75, 105-108 (1995). .

5. mapping fermionic bath DFT and DMFT Density functional theory observable of interest is the electron density Dynamical mean field theory: observable of interest is the local Green's function (on the lattice uniquely defined) DMFT approximation exact BK functional

6. Spectral density functional theory: use local Green's function (spectral function) instead of local density Spectral density functional theory observable of interest is the "local" Green's functions LDA+DMFT: basic idea: sum-up all local diagrams for electrons in correlated orbitals LDA+U corresponds to LDA+DMFT when impurity is solved in the Hartree Fock approximation

7. * LDA local in localized LMTO base DMFT SCC * Impurity solver Impurity problem (14x14): LDA+DMFT Calculation

8. weakly correlated strongly correlated metal Mott isolator LDA bandwidth Coulomb interaction

9. f7 L=0,S=7/2 J=7/2 f5 L=5,S=5/2 J=5/2 f1 L=3,S=1/2 J=5/2 f6 L=3,S=3 J=0 Overview

10. Cerium

11. Ce overview  isostructural phase transition ends in a critical point at (T=600K, P=2GPa)  (fcc) phase [ magnetic moment (Curie-Wiess law), large volume, stable high-T, low-p]   (fcc) phase [ loss of magnetic moment (Pauli-para), smaller volume, stable low-T, high-p] with large volume collapse v/v  15 • Transition is 1.order • ends with CP very similar to gas-liquid condesation of water

12. LDA and LDA+U ferromagnetic f DOS total DOS

13. LDA+DMFT alpha DOS TK(exp)=1000-2000K

14. LDA+DMFT gamma DOS TK(exp)=60-80K

15. Photoemission&experiment Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): Fenomenological Landau approach:

16. Optical conductivity + * + K. Haule, V. Oudovenko, S. Y. Savrasov, and G. KotliarPhys. Rev. Lett. 94, 036401 (2005) *

17. Americium

18. Americium Mott Transition? "soft" phase "hard" phase A.Lindbaum*, S. Heathman, K. Litfin, and Y. Méresse, Phys. Rev. B 63, 214101 (2001) J.-C. Griveau, J. Rebizant, G. H. Lander, andG.KotliarPhys. Rev. Lett. 94, 097002 (2005)

19. Am within LDA+DMFT S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)

20. Am within LDA+DMFT very different "soft" localized phase from g Ce not in local moment regime since J=0 (no entropy) Comparisson with experiment nf=6 nf=6.2 * *J. R. Naegele, L. Manes, J. C. Spirlet, and W. MüllerPhys. Rev. Lett. 52, 1834-1837 (1984) "Hard" phase similar to a Ce, Kondo physics due to hybridization, however, nf still far from Kondo regime Different from Sm! from J=0 to J=7/2

21. high Tc's

22. Models of high Tc's cluster in real space cluster in k space

23. Coherence scale and Tc

24. optics

25. power laws Nature 425, 271-274 (2003)

26. optics mass and plasma w Basov, cond-mat/0509307

27. SC density of states

28. Kinetic and Exchange energy cond-mat/0503073

29. 41meV resonance

30. pseudoparticle insights

31. Conclusions • In many correlated f metals, single site LDA+DMFT gives the zeroth order picture • 2D models of high-Tc require cluster of sites. Optimally doped regime can be well described with smallest cluster 2x2.

32. Partial DOS 4f Z=0.33 5d 6s

33. More complicated f systems • Hunds coupling is important when more than one electron in the correlated (f) orbital • Spin orbit coupling is very small in Ce, while it become important in heavier elements The complicated atom embedded into fermionic bath (with crystal fileds) is a serious chalange so solve! Coulomb interaction is diagonal in the base of total LSJ -> LS base while the SO coupling is diagonal in the j-base -> jj base Eigenbase of the atom depends on the strength of the Hund's couling and strength of the spin-orbit interaction

34. Classical theories Mott transition (B. Johansson, 1974): Hubbard model f electrons insulating changes and causes Mott tr. spd electrons pure spectators Anderson (impurity) model Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): hybridization with spd electrons is crucial (Lavagna, Lacroix and Cyrot, 1982) changes → chnange of TK bath f electrons in local moment regime either constant or taken from LDA and rescaled Fenomenological Landau approach:

35. ab initio calculation LDA+DMFT is self-consistently determined bath for AIM contains tff and Vfd hopping • Kondo volume colapse model resembles DMFT picture: • Solution of the Anderson impurity model→ Kondo physics • Difference: with DMFT the lattice problem is solved (and therefore Δ must self-consistently determined)while in KVC Δ is calculated for a fictious impurity (and needs to be rescaled to fit exp.) • In KVC scheme there is no feedback on spd bans, hence optics is not much affected.

36. An example Atomic physics of selected Actinides