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IJS Strongly correlated materials from Dynamical Mean Field Perspective. DMFT(SUNCA method) two-band Hubbard model Bethe lattice, U=4D Thanks to: G.Kotliar, S. Savrasov, V. Oudovenko IJS Overview • Application of DMFT to real materials (LDA+DMFT) • Extensions of DMFT to clusters and its application to models for high-Tc IJS 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] mapping fermionic bath IJS 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). . IJS 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) exact BK functional mapping fermionic bath DMFT approximation IJS Spectral density functional theory 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 LDA+U corresponds to LDA+DMFT when impurity is solved in the Hartree Fock approximation IJS LDA+DMFT Calculation LDA DMFT SCC * * Impurity solver local in localized LMTO base Impurity problem (14x14): IJS weakly correlated strongly correlated metal LDA bandwidth Mott isolator Coulomb interaction IJS Overview f5 L=5,S=5/2 J=5/2 f7 L=0,S=7/2 J=7/2 f1 L=3,S=1/2 J=5/2 f6 L=3,S=3 J=0 IJS Cerium IJS Ce overview isostructural phase transition ends in a critical point at (T=600K, P=2GPa) g (fcc) phase [ magnetic moment (Curie-Wiess law), large volume, stable high-T, low-p] a (fcc) phase [ loss of magnetic moment (Pauli-para), smaller volume, stable low-T, high-p] with large volume collapse v/v 15 volumes exp. 28Å3 a 34.4Å3 g LDA 24.7Å3 LDA+U 35.2Å3 •Transition is 1.order •ends with CP very similar to gasliquid condesation of water IJS LDA and LDA+U ferromagnetic volumes exp. 28Å3 a 34.4Å3 g LDA 24.7Å3 LDA+U 35.2Å3 f DOS total DOS IJS LDA+DMFT alpha DOS TK(exp)=1000-2000K IJS LDA+DMFT gamma DOS TK(exp)=60-80K IJS Photoemission&experiment Kondo volume colapse (J.W. Allen, R.M. Martin, 1982): Fenomenological Landau approach: IJS Optical conductivity + * + K. Haule, V. Oudovenko, S. Y. Savrasov, and G. Kotliar Phys. Rev. Lett. 94, 036401 (2005) * IJS Americium IJS Americium Mott Transition? "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) IJS Am within LDA+DMFT S. Y. Savrasov, K. Haule, and G. Kotliar Phys. Rev. Lett. 96, 036404 (2006) IJS Am within LDA+DMFT very different "soft" localized phase from g Ce not in local moment regime since J=0 (no entropy) nf=6.2 Comparisson with experiment nf=6 * *J. R. Naegele, L. Manes, J. C. Spirlet, and W. Müller Phys. 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 IJS high Tc's IJS Models of high Tc's cluster in k space cluster in real space IJS Coherence scale and Tc IJS optics IJS power laws Nature 425, 271-274 (2003) IJS optics mass and plasma w Basov, cond-mat/0509307 IJS SC density of states IJS Kinetic and Exchange energy cond-mat/0503073 IJS 41meV resonance IJS pseudoparticle insights 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. IJS Partial DOS 4f 5d 6s Z=0.33 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 IJS 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 f electrons in local moment regime bath either constant or taken from LDA and rescaled Fenomenological Landau approach: IJS LDA+DMFT ab initio calculation bath for AIM is self-consistently determined 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 selfconsistently 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. IJS An example Atomic physics of selected Actinides IJS