ijs strongly correlated materials from dynamical mean field perspective. thanks to: g.kotliar, s....
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![Page 1: IJS Strongly correlated materials from Dynamical Mean Field Perspective. Thanks to: G.Kotliar, S. Savrasov, V. Oudovenko DMFT(SUNCA method) two-band Hubbard](https://reader030.vdocument.in/reader030/viewer/2022032523/56649d775503460f94a59766/html5/thumbnails/1.jpg)
IJS
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
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IJS Overview
• Application of DMFT to real materials (LDA+DMFT)
• Extensions of DMFT to clusters and its application to models for high-Tc
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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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IJS
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
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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
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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
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IJS LDA+DMFT Calculation
local in localized LMTO base
Impurity problem (14x14):
LDA
Impurity solver
DMFT SCC *
*
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IJS
weakly correlated Mott isolatorstrongly correlated metal
Coulomb interactionLDA bandwidth
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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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IJS
Cerium
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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
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IJS LDA and LDA+U
f DOStotal DOSvolumes exp. LDA LDA+U
28Å3 24.7Å3
34.4Å3 35.2Å3
ferromagnetic
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IJS LDA+DMFT alpha DOS
TK(exp)=1000-2000K
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IJS LDA+DMFT gamma DOS
TK(exp)=60-80K
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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):
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IJS Optical conductivity
*
*
+
+ K. Haule, V. Oudovenko, S. Y. Savrasov, and G. Kotliar Phys. Rev. Lett. 94, 036401 (2005)
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IJS
Americium
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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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IJS
S. Y. Savrasov, K. Haule, and G. KotliarPhys. Rev. Lett. 96, 036404 (2006)
Am within LDA+DMFT
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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!
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IJS high Tc's
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IJS Models of high Tc's
cluster in k space cluster in real space
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IJS Coherence scale and Tc
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IJS optics
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IJS power laws
Nature 425, 271-274 (2003)
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IJS
Basov, cond-mat/0509307
optics mass and plasma w
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IJS SC density of states
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IJS
cond-mat/0503073
Kinetic and Exchange energy
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IJS 41meV resonance
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IJS pseudoparticle insights
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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.
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IJS Partial DOS
4f
5d
6s
Z=0.33
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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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IJS
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:
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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.
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IJS An example
Atomic physics of selected Actinides
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IJS