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Electronic Structure of Strongly Correlated Electron Materials: A Dynamical Mean Field Perspective. Collaborators: G.Kotliar, Ji-Hoon Shim, S. Savrasov. Kristjan Haule , Physics Department and Center for Materials Theory Rutgers University Rutgers University. - PowerPoint PPT Presentation
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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