Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov

Kristjan Haule, Physics Department and

Center for Materials TheoryRutgers University Rutgers University

Electronic Structure of Strongly CorreElectronic Structure of Strongly Correlated Electron Materials: A Dynamicalated Electron Materials: A Dynamica

l Mean Field Perspective.l Mean Field Perspective.

Miniworkshop on New States of Stable and Unstable Quantum Matter, Trst 2006

• Application of DMFT to real materials (Spectral density functional approach). Examples: – alpha to gamma transition in Ce, optics near the

temperature driven Mott transition. – Mott transition in Americium under pressure– Antiferromagnetic transition in Curium

• Extensions of DMFT to clusters. Examples:– Superconducting state in t-J the model– Optical conductivity of the t-J model

OverviewOverview

V2O3Ni2-xSex organics

Universality of the Mott transitionUniversality of the Mott transition

First order MIT

Critical point

Crossover: bad insulator to bad metal

1B HB model 1B HB model (DMFT):(DMFT):

Coherence incoherence crossover in the Coherence incoherence crossover in the

1B HB model (DMFT)1B HB model (DMFT)

Phase diagram of the HM with partial frustration at half-fillingPhase diagram of the HM with partial frustration at half-filling

M. Rozenberg et.al., Phys. Rev. Lett. M. Rozenberg et.al., Phys. Rev. Lett. 7575, 105 (1995)., 105 (1995).

DMFT + electronic structure methodDMFT + electronic structure method

Effective (DFT-like) single particle Spectrum consists of delta like peaks

Spectral density usually contains renormalized quasiparticles and Hubbard bands

Basic idea of DMFT: reduce the quantum many body problem to a one site or a cluster of sites problem, in a medium of non interacting electrons obeying a self-consistency condition. (A. Georges et al., RMP 68, 13 (1996)).

DMFT in the language of functionals: DMFT sums up all local diagrams in BK functional

Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated bands (s,p): use LDA or GWFor correlated bands (f or d): with DMFT add all local diagrams

f1

L=3,S=1/2 J=5/2

f6

L=3,S=3 J=0

How good is single site DMFT for f systems?

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

Cerium

Ce overview

volumes exp. LDA LDA+U 28Å3 24.7Å3

34.4Å3 35.2Å3

•Transition is 1.order•ends with CP

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

LDA and LDA+U

f DOStotal DOSvolumes exp. LDA LDA+U

28Å3 24.7Å3

34.4Å3 35.2Å3

ferromagnetic

LDA+DMFT alpha DOS

TK(exp)=1000-2000K

LDA+DMFT gamma DOS

TK(exp)=60-80K

Photoemission&experiment

Fenomenological approachdescribes well the transition

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

•A. Mc Mahan K Held and R. Scalettar (2002)

•K. Haule V. Udovenko and GK. (2003)

Optical conductivity

*

+

+ K. Haule, et.al., Phys. Rev. Lett. 94, 036401 (2005)

* J.W. van der Eb, A.B. Ku’zmenko, and D. van der Marel, Phys. Rev. Lett. 86, 3407 (2001)

Americium

Americium

"soft" phase

f localized

"hard" phase

f bonding

Mott Transition?

f6 -> L=3, S=3, J=0

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

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

Am within LDA+DMFT

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

F(0)=4.5 eV F(2)=8.0 eVF(4)=5.4 eV F(6)=4.0 eV

Large multiple effects:

Am within LDA+DMFT

nf=6

Comparisson with experiment

from J=0 to J=7/2

•“Soft” phase very different from Cenot 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!

Exp: J. R. Naegele, L. Manes, J. C. Spirlet, and W. MüllerPhys. Rev. Lett. 52, 1834-1837 (1984)

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

V=V0 Am IV=0.76V0 Am IIIV=0.63V0 Am IV

Curie-Weiss

Tc

Trends in Actinidesalpa->delta volume collapse transition

Same transition in Am under pressure

Curium has large magnetic moment and orders antif.

F0=4,F2=6.1

F0=4.5,F2=7.15

F0=4.5,F2=8.11

EELS & XASco

revale

nce

4d3/2

4d5/2

5f5/2

5f7/2

Exci

tati

ons

from

4d c

ore

to 5

f vale

nce

Electron energy loss spectroscopy (EELS) orX-ray absorption spectroscopy (XAS)

Branching ration B=A5/2/(A5/2+A3/2)

Energy loss [eV]

Core splitting~50eV

4d5/2->5f7/2

4d3/2->5f5/2

2/3<l.s>=-5/2(14-nf)(B-B0) B0~3/5

Measures unoccupied valence 5f statesProbes high energy Hubbard bands!

gives constraint on nf

for given nf, determines <l.s>

LS versus jj coupling in Actinides

K.T.Moore, et.al.,PRB in press, 2006G. Van der Laan, et.al, PRL 93,27401 (2004)J.G. Tobin, et.al, PRB 72, 85109 (2005)

•Occupations non-integer except Cm

•Close to intermediate coupling

•Am under pressure goes towards LS

•Delocalization in U & Pu-> towards LS

•Curium is localized, but close to LS!=7.9B not =4.2B

What is captured by single site DMFT?

•Captures volume collapse transition (first order Mott-like transition)•Predicts well photoemission spectra, optics spectra,

total energy at the Mott boundary•Antiferromagnetic ordering of magnetic moments,

magnetism at finite temperature•Qualitative explanation of mysterious phenomena, such as

the anomalous raise in resistivity as one applies pressure in Am,..

Beyond single site DMFT

What is missing in DMFT?

•Momentum dependence of the self-energy m*/m=1/Z

•Various orders: d-waveSC,…

•Variation of Z, m*, on the Fermi surface

•Non trivial insulator (frustrated magnets)

•Non-local interactions (spin-spin, long range Columb,correlated hopping..)

Present in DMFT:•Quantum time fluctuations

Present in cluster DMFT:•Quantum time fluctuations•Spatially short range quantum fluctuations

The simplest model of high Tc’s

t-J, PW Anderson

Hubbard-Stratonovich ->(to keep some out-of-cluster quantum fluctuations)

BK Functional, Exact

cluster in k space cluster in real space

t’=0

Phase diagram

What can we learn from “small” Cluster-DMFT?

Insights into superconducting state (BCS/non-BCS)?

J. E. Hirsch, Science, 295, 5563 (2001)

BCS: upon pairing potential energy of electrons decreases, kinetic energy increases(cooper pairs propagate slower)Condensation energy is the difference

non-BCS: kinetic energy decreases upon pairing(holes propagate easier in superconductor)

D van der Marel, Nature 425, 271-274 (2003)

cond-mat/0601478

Optical conductivity

overdoped

optimally doped

Bi2212

~1eVWeight bigger in SC,

K decreases (non-BCS)

Weight smaller in SC, K increases (BCS-like)

Optical weight, plasma frequency

F. Carbone et.al, cond-mat/0605209

Hubbard model

DrudeU

t2/U

t-J model

J

Drude

no-U

Experiments

intraband interband transitions

~1eV

Excitations into upper Hubbard band

Kinetic energy in Hubbard model:•Moving of holes•Excitations between Hubbard bands

Kinetic energy in t-J model•Only moving of holes

Hubbard versus t-J model

Phys Rev. B 72, 092504 (2005)

cluster-DMFT, cond-mat/0601478

Kinetic energy change

Kinetic energy decreases

Kinetic energy increases

Kinetic energy increases

Exchange energy decreases and gives

largest contribution to condensation energy

cond-mat/0503073

electrons gain energy due to exchange energyholes gain kinetic energy (move faster)

underdoped

electrons gain energy due to exchange energyhole loose kinetic energy (move slower)

overdoped

BCS likesame as RVB (see P.W. Anderson Physica C, 341, 9 (2000),

or slave boson mean field (P. Lee, Physica C, 317, 194 (1999)

Kinetic energy upon condensation

J

J J

J

Pengcheng et.al., Science 284, (1999)

YBa2Cu3O6.6 (Tc=62.7K)

41meV resonance

local susceptibility

•Resonance at 0.16t~48meV•Most pronounced at optimal doping•Second peak shifts with doping (at 0.38~120meV opt.d.) and changes below Tc – contribution to condensation energy

Optics mass and plasma frequency

Extended Drude model

•In sigle site DMFT plasma frequency vanishes as 1/Z (Drude shrinks as Kondo peak shrinks) at small doping

•Plasma frequency vanishes because the active (coherent) part of

the Fermi surface shrinks •In cluster-DMFT optics mass constant at

low doping doping ~ 1/Jeff

line: cluster DMFT (cond-mat 0601478),symbols: Bi2212, F. Carbone et.al, cond-mat/0605209

• LDA+DMFT can describe interplay of lattice and electronic structure near Mott transition. Gives physical connection between spectra, lattice structure, optics,.... – Allows to study the Mott transition in open and

closed shell cases. – In elemental actinides and lanthanides single site

LDA+DMFT gives the zeroth order picture• 2D models of high-Tc require cluster of sites. Some

aspects of optimally doped, overdoped and slightly underdoped regime can be described with cluster DMFT on plaquette:– Evolution from kinetic energy saving to BCS kinetic

energy cost mechanism

Conclusions

Partial DOS

4f

5d

6s

Z=0.33

Optimal doping: Coherence scale seems

to vanish

Tc

underdoped

overdoped

optimally

scattering at Tc

Pseudoparticle insight

N=4,S=0,K=0

N=4,S=1,K=()

N=3,S=1/2,K=(,0)

N=2,S=0,K=0

A()

’’()PH symmetry,

Large