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Strongly correlated materials from Strongly correlated materials from

Dynamical Mean Field Perspective.Dynamical Mean Field Perspective.

Thanks to: G.Kotliar, S. Savrasov, V. Oudovenko

DMFT(SUNCA method)

two-band Hubbard model

Bethe lattice, U=4D

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

mappingmapping

fermionic bathfermionic 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]

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

Coherence incoherence crossover in a model

IJS DFT and DMFT

Density functional theory

Dynamical mean field theory:

observable of interest is the electron densityobservable of interest is the electron density

observable of interest is the local Green's function observable of interest is the local Green's function

(on the lattice(on the lattice uniquely defined uniquely defined))

fermionic bathfermionic bath

mappingmapping

exact BK

functional

DMFT

approximation

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 densityobservable of interest observable of interest

is the "local" is the "local"

Green's functionsGreen's functions

LDA+DMFT: basic idea: sum-up all local diagrams for electrons in correlated orbitals

IJS LDA+DMFT Calculation

local in localized LMTO base

Impurity problem (14x14):

LDA

Impurity solver

DMFT SCC *

*

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weakly correlated Mott isolatorstrongly correlated metal

Coulomb interactionLDA bandwidth

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

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Cerium

IJS Ce overview

volumes exp. LDA LDA+U 28Å3 24.7Å3

34.4Å3 35.2Å3

•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

IJS LDA and LDA+U

f DOStotal DOSvolumes exp. LDA LDA+U

28Å3 24.7Å3

34.4Å3 35.2Å3

ferromagnetic

IJS LDA+DMFT alpha DOS

TK(exp)=1000-2000K

IJS LDA+DMFT gamma DOS

TK(exp)=60-80K

IJS Photoemission&experiment

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

IJS Optical conductivity

*

*

+

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

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Americium

IJS Americium

"soft" phase

"hard" phase

J.-C. Griveau, J. Rebizant, G. H. Lander, and G.KotliarPhys. Rev. Lett. 94, 097002 (2005)

A.Lindbaum*, S. Heathman, K. Litfin, and Y. Méresse, Phys. Rev. B 63, 214101 (2001)

Mott Transition?

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S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)

Am within LDA+DMFT

IJS Am within LDA+DMFT

nf=6

Comparisson with experiment

*J. R. Naegele, L. Manes, J. C. Spirlet, and W. MüllerPhys. 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

nf=6.2

Different from Sm!

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)

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Basov, cond-mat/0509307

optics mass and plasma w

IJS SC density of states

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cond-mat/0503073

Kinetic and Exchange energy

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 The complicated atom embedded into fermionic

bath (with crystal fileds) is a serious chalange so solve!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

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Mott transition (B. Johansson, 1974):Mott transition (B. Johansson, 1974):

Kondo volume colapse (J.W. Allen, R.M. Martin, 1982):Kondo volume colapse (J.W. Allen, R.M. Martin, 1982):

Classical theories

Hubbard modelHubbard model

Anderson (impurity) modelAnderson (impurity) model

changes and causes Mott tr.changes and causes Mott tr.

changes changes →→ chnange of T chnange of TKK

bath

either constant or

taken from LDA and rescaled

spd electrons pure spectatorsspd electrons pure spectators

hybridization with spd electrons is crucialhybridization with spd electrons is crucial

f electrons insulating

f electrons in local moment regime

(Lavagna, Lacroix and Cyrot, 1982)(Lavagna, Lacroix and Cyrot, 1982)

Fenomenological Landau approach:

IJS LDA+DMFT

ab initio calculationab initio calculation

is self-consistently determinedis self-consistently determined

contains tcontains tffff and V and Vfdfd hopping hopping

bath for AIMbath for AIM

Kondo volume colapse model resembles DMFT picture:Kondo volume colapse model resembles DMFT picture:

Solution of the Solution of the Anderson impurity modelAnderson impurity model → → Kondo physicsKondo physics

DifferenceDifference: : with DMFT the lattice problem is solved (and therefore 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.

IJS An example

Atomic physics of selected Actinides

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