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

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Electronic structure of Strongly Correlated
Materials A Dynamical Mean Field Perspective.
Kristjan Haule, Physics Department and Center
for Materials Theory Rutgers University

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

ES 07 - Raleigh
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Standard theory of solids
Band Theory electrons as waves Rigid
non-dipersive band
picture
En(k) versus k Landau Fermi Liquid Theory
applicable Very powerful quantitative tools
LDA,LSDA,GW

• Predictions
• total energies,
• stability of crystal phases
• optical transitions

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Strong correlation Standard theory fails

• Fermi Liquid Theory does NOT work . Need new
  concepts to replace rigid bands picture!
• Breakdown of the wave picture. Need to
  incorporate a real space perspective (Mott).
• Non perturbative problem.

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Universality of the Mott transition
Crossover bad insulator to bad metal
Critical point
First order MIT
Ni2-xSex
k organics
V2O3
1B HB model (DMFT)
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Localization
Delocalization
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Basic questions

• How to describe the physics of strong
  correlations close to the Mott boundary?
• How to computed spectroscopic quantities (single
  particle spectra, optical conductivity phonon
  dispersion) from first principles?
• New concepts, new techniques.. DMFT maybe
  simplest approach to meet this challenge

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DMFT electronic structure method
Basic idea of DMFT reduce the quantum many body
problem to a problem of an atom in a conduction
band, which obeys DMFT 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 DMFTelectronic structure method
(LDA or GW) For less correlated bands (s,p)
use LDA or GW For correlated bands (f or d) with
DMFT add all local diagrams
(G. Kotliar S. Savrasov K.H., V. Oudovenko O.
Parcollet and C. Marianetti, RMP 2006).
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LDADMFT
(G. Kotliar et.al., RMP 2006).
observable of interest is the "local Green's
functions (spectral function)
Exact functional of the local Greens function
exists, its form unknown!
Currently Feasible approximations LDADMFT
Variation gives st. eq.
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Exact QMC impurity solver, expansion in terms
of hybridization
K.H. Phys. Rev. B 75, 155113 (2007)
P. Werner, Phys. Rev. Lett. 97, 076405 (2006)
General impurity problem
Diagrammatic expansion in terms of hybridization
D Metropolis sampling over the diagrams

• Exact method samples all diagrams!
• Allows correct treatment of multiplets

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Volume of actinides
Trivalent metals with nonbonding f shell
Partly localized, partly delocalized
fs participate in bonding
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Anomalous Resistivity
Maximum metallic resistivity
se2 kF/h
Fournier Troc (1985)
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Dramatic increase of specific heat
Heavy-fermion behavior in an element
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NO Magnetic moments!
Pauli-like from melting to lowest T
No curie Weiss up to 600K
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Curium versus Plutonium
nf6 -gt J0 closed shell (j-j 6 e- in 5/2
shell) (LS L3,S3,J0)
One more electron in the f shell
One hole in the f shell

• Magnetic moments! (Curie-Weiss law at high T,
• Orders antiferromagnetically at low T)
• Small effective mass (small specific heat
  coefficient)
• Large volume

• No magnetic moments,
• large mass
• Large specific heat,
• Many phases, small or large volume

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• Standard theory of solids
• DFT
• All Cm, Am, Pu are magnetic in LSDA/GGA
• LDA Pu(m5mB), Am (m6mB) Cm (m4mB)
• Exp Pu (m0), Am (m0) Cm (m7.6mB)
• Non magnetic LDA/GGA predicts volume up to 30
  off.
• In atomic limit, Am non-magnetic, but Pu magnetic
  with spin 5mB

• Many proposals to explain why Pu is non magnetic
• Mixed level model (O. Eriksson, A.V. Balatsky,
  and J.M. Wills) (5f)4 conf. 1itt.
• LDAU, LDAUFLEX (Shick, Anisimov, Purovskii)
  (5f)6 conf.
• Cannot account for anomalous transport and
  thermodynamics

• Can LDADMFT account for anomalous properties of
  actinides?
• Can it predict which material is magnetic and
  which is not?

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Very strong multiplet splitting
Atomic multiplet splitting crucial -gt splits
Kondo peak
N Atom F2 F4 F6 x
92 U 8.513 5.502 4.017 0.226
93 Np 9.008 5.838 4.268 0.262
94 Pu 8.859 5.714 4.169 0.276
95 Am 9.313 6.021 4.398 0.315
96 Cm 10.27 6.692 4.906 0.380
Increasing Fs an SOC
Used as input to DMFT calculation - code of R.D.
Cowan
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Starting from magnetic solution, Curium develops
antiferromagnetic long range order below Tc
above Tc has large moment (7.9mB close to LS
coupling) Plutonium dynamically restores symmetry
-gt becomes paramagnetic
J.H. Shim, K.H., G. Kotliar, Nature 446, 513
(2007).
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Multiplet structure crucial for correct Tk in Pu
(800K) and reasonable Tc in Cm (100K)
Without F2,F4,F6 Curium comes out paramagnetic
heavy fermion Plutonium weakly
correlated metal
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Valence histograms
Density matrix projected to the atomic
eigenstates of the f-shell (Probability for
atomic configurations)
f electron fluctuates between these atomic states
on the time scale th/Tk (femtoseconds)

• Probabilities
• 5 electrons 80
• 6 electrons 20
• 4 electrons lt1

One dominant atomic state ground state of the
atom
J.H. Shim, K. Haule, G. Kotliar, Nature 446, 513
(2007).
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Fingerprint of atomic multiplets - splitting of
Kondo peak
Gouder , Havela PRB 2002, 2003
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Photoemission and valence in Pu
ground state gt a f5(spd)3gt b f6 (spd)2gt
approximate decomposition
Af(w)
f5lt-gtf6
f6-gtf7
f5-gtf4
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Probe for Valence and Multiplet structure
EELSXAS
Electron energy loss spectroscopy (EELS) or X-ray
absorption spectroscopy (XAS)
A plot of the X-ray absorption as a function of
energy
Core splitting50eV
Measures unoccupied valence 5f states Probes high
energy Hubbard bands!
Branching ration BA5/2/(A5/2A3/2)
BB0 - 4/15ltl.sgt/(14-nf)
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2/3ltl.sgt-5/2(B-B0) (14-nf)
LDADMFT
a G. Van der Laan et al., PRL 93, 97401
(2004). b G. Kalkowski et al., PRB 35, 2667
(1987) c K.T. Moore et al., PRB 73, 33109
(2006). d K.T. Moore et al., PRL in press
One measured quantity B, two unknowns Close to
atom (IC regime) Itinerancy tends to decrease
ltl.sgt
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Specific heat
Could Pu be close to f6 like Am?
(Shick, Anisimov, Purovskii) (5f)6 conf
Purovskii et.al. cond-mat/0702342
f6 configuration gives smaller g in d Pu than a Pu
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Americium
f6 -gt L3, S3, J0
Mott Transition?
"soft" phase f localized
"hard" phase f bonding
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)
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Am within LDADMFT
F(0)4.5 eV F(2)8.0 eV F(4)5.4 eV F(6)4.0 eV
Large multiple effects
S. Y. Savrasov, K.H., and G. KotliarPhys. Rev.
Lett. 96, 036404 (2006)
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Am within LDADMFT
from J0 to J7/2
Comparisson with experiment
VV0 Am I
V0.76V0 Am III
V0.63V0 Am IV
nf6
nf6.2
Exp J. R. Naegele, L. Manes, J. C. Spirlet, and
W. MüllerPhys. Rev. Lett. 52, 1834-1837 (1984)

• Soft phase not in local moment regime
• since J0 (no entropy)

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

• "Hard" phase similar to d Pu,
• Kondo physics due to hybridization, however,
• nf still far from Kondo regime

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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
• Branching ratios in XAS experiments, Dynamic
  valence fluctuations,
• Specific heat
• Gap in charge transfer insulators like PuO2

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Beyond single site DMFT
What is missing in DMFT?

• Momentum dependence of the self-energy m/m1/Z
• Various orders d-waveSC,
• Variation of Z, m,t on the Fermi surface
• Non trivial insulator (frustrated magnets)
• Non-local interactions (spin-spin, long range
  Columb,correlated hopping..)

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

• Present in DMFT
• Quantum time fluctuations

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Plaquette DMFT for the Hubbard model as relevant
for cuprates
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Complicated Fermi surface evolution with
temperature
underoped phase fermi arcs
Superconducting phase- banana like Fermi surface
arcs decrease with T
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Conclusion

• Pu and Am (under pressure) are unique strongly
  correlated elements. Unique mixed valence.
• They require, new concepts, new computational
  methods, new algorithms, DMFT!
• Cluster extensions of DMFT can describe many
  features of cuprates including superconductivity
  and gapping of fermi surface (pseudogap)

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Many strongly correlated compounds await the
explanation CeCoIn5, CeRhIn5, CeIrIn5
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Photoemission of CeIrIn5
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Photoemission of CeIrIn5
LDADMFT DOS
Comparison to experiment
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Optics of CeIrIn5
LDADMFT
K.S. Burch et.al., cond-mat/0604146
Experiment
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Optimal doping Coherence scale seems to vanish
underdoped
scattering at Tc
optimally
overdoped
Tc
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New continuous time QMC, expansion in terms of
hybridization
General impurity problem
Diagrammatic expansion in terms of hybridization
D Metropolis sampling over the diagrams
Contains all Non-crossing and all crossing
diagrams! Multiplets correctly treated
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Conclusions

• LDADMFT 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 actinides and their compounds, single site
  LDADMFT gives the zero-th order picture
• 2D models of high-Tc require cluster of sites.
  Some aspects of optimally doped regime can be
  described with cluster DMFT on plaquette
• Large scattering rate in normal state close to
  optimal doping

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Basic questions

• How does the electron go from being localized to
  itinerant.
• How do the physical properties evolve.
• How to bridge between the microscopic information
  (atomic positions) and experimental measurements.
• New concepts, new techniques.. DMFT simplest
  approach to meet this challenge

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Coherence incoherence crossover in the 1B HB
model (DMFT)
Phase diagram of the HM with partial frustration
at half-filling M. Rozenberg et.al., Phys. Rev.
Lett. 75, 105 (1995).
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Singlet-type Mott state (no entropy) goes mixed
valence under pressure -gt Tc enhanced (Capone
et.al, Science 296, 2364 (2002))
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Overview

• DMFT in actinides and their compounds (Spectral
  density functional approach).
• Examples
• Plutonium, Americium, Curium.
• Compounds PuAm
• Observables
• Valence, Photoemission, and Optics, X-ray
  absorption

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Why is Plutonium so special?
Heavy-fermion behavior in an element
Typical heavy fermions (large mass-gtsmall
Tk Curie Weis at TgtTk)
No curie Weiss up to 600K
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Why is Plutonium so special?
Heavy-fermion behavior in an element
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Overview of actinides
Many phases
25 increase in volume between a and d phase
Two phases of Ce, a and g with 15 volume
difference
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f-sumrule for core-valence conductivity
Similar to optical conductivity
Current
Expressed in core valence orbitals
The f-sumrule
can be expressed as
Branching ration BA5/2/(A5/2A3/2)
BB0 - 4/15ltl.sgt/(14-nf)
B03/5

• Branching ratio depends on
• average SO coupling in the f-shell ltl.sgt
• average number of holes in the f-shell nf

A5/2 area under the 5/2 peak
B.T. Tole and G. van de Laan, PRA 38, 1943 (1988)
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Optical conductivity
Pu similar to heavy fermions (Kondo type
conductivity) Scale is large MIR peak at
0.5eV PuO2 typical semiconductor with 2eV gap,
charge transfer
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Spectral density functional theory
(G. Kotliar et.al., RMP 2006).
observable of interest is the "local Green's
functions (spectral function)
Currently feasible approximations LDADMFT
Variation gives st. eq.
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Pu-Am mixture, 50Pu,50Am
Lattice expands -gt Kondo collapse is expected
Our calculations suggest charge transfer Pu d
phase stabilized by shift to mixed valence
nf5.2-gtnf5.4
Hybridization decreases, but nf increases, Tk
does not change significantly!
f6 Shorikov, et al., PRB 72, 024458 (2005)
Shick et al, Europhys. Lett. 69, 588 (2005).
Pourovskii et al., Europhys. Lett. 74, 479
(2006).
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