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

3. IJS Dynamical Mean Field Theorymapping fermionic bath 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. IJS Phase diagram of a Hubbard model with partial frustration at integer filling. M. Rozenberg et.al., Phys. Rev. Lett. 75, 105-108 (1995)..Phys. Rev. Lett. 75, 105-108 (1995). Coherence incoherence crossover in a model

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

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

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

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

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

10. IJS Cerium

11. IJS Ce overview volumesexp.LDALDA+U  28Å 3 24.7Å 3  34.4Å 3 35.2Å 3 Transition is 1.order ends with CP very similar to gas- liquid condesation of water  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 

12. IJS LDA and LDA+U f DOS total DOS volumesexp.LDALDA+U  28Å 3 24.7Å 3  34.4Å 3 35.2Å 3 ferromagnetic

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

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

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

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

17. IJS Americium

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

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

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

21. IJS high Tc's

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

23. IJS Coherence scale and Tc

24. IJS optics

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

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

27. IJS SC density of states

28. IJS cond-mat/0503073 Kinetic and Exchange energy

29. IJS 41meV resonance

30. IJS pseudoparticle insights

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

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

35. IJS LDA+DMFT ab initio calculation is self-consistently determined contains t ff and V fd hopping bath for AIM 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 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. IJS An example Atomic physics of selected Actinides

37. IJS