Transcript Strongly Correlated Electron Materials

Strongly Correlated Electron Materials: Some DMFT
Concepts and Applications
Gabriel Kotliar
and Center for Materials Theory
Colloquium University of Toronto Canada
March 3rd 2011
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“Standard Model of Solids “ Band Theory. Fermi Liquid
Theory (Landau 1957).
Density Functional Theory (Kohn Sham 1964) energy functional of the
density.
- Ñ / 2 + VKS ( r )[r ] y kj = ekj y kj
2
r (r ) =
å
ekj < 0
y kj *(r )y kj (r )
Reference Frame for
Weakly Correlated
Systems.
Starting point for perturbation theory in the screened Coulomb interactions
(Hedin 1965)
G
1
1
0KS
 G
+[
-
VKS
Phys. Rev. Lett. 93, 126406 (2004).
Many other properties can be computed,
transport, optics, phonons, etc…
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]
Cuprate Experimental Phase diagram

3
e 2 k F (k F l )
h
Anomalously
small
conductivities
Damascelli, Shen, Hussain, RMP 75, 473 (2003)
Anomalous resistivities
Sr2RuO4
C. Urano et. al. PRL 85, 1052
(2000)
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Probing Electronic Structure:Photoemission
e
A(k, w)
A(k, w)
w
a) Weak correlations
b)Strong correlation: fermi liquid parameters
can’t be evaluated in perturbation theory
or fermi liquid theory does not work.
Angle integrated spectra
 dk Im G(w, k )  A(w )
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Many other spectroscopic tools to “see”
correlated electrons !
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Shining light on correlated electrons. Optical conductivity.
Failure of the Standard
Model: Anomalous Spectral Weight Transfer


0
 (w )dw
Very Non local transfer of spectral weight in FeSi
D. Van der Marel et.al (2005) [ 1 ev 800 cm-1]
= Neff (T,  )depends on T
Optical Conductivity
Schlesinger t.al (1993)
Weight does not recover up to 5 ev.

Other probes for correlated electrons X-rays, neutrons, electrons, the kitchen sink, theory
……….
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How to Make Correlated materials ?
Put open shell in a cage
transition metal ion
Oxygen
Transition metal ions
Cage : e.g 6 oxygen atoms (octahedra)Rare earth ions
or other ligands/geometry
Actinides
Transition metal (open shell )
Build crystal with this building block
or build layers separated by spacers
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VO2
La1-xSrxMnO3
Room
temperature
MIT
Colossal
Magnetoresistance
LixCoO2, NaxCoO2
Battery materials
Thermoelectrics
La1-xSrxCuO4
High temperature
superconductor
How to find interesting correlated materials ?
+ Edisonian approach
Serendipity
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An aptitude for making desirable discoveries by accident
The Edisonian approach to innovation is characterized by trial
and error discovery rather than a systematic theoretical
approach. (e.g. carbon microphone, basis of telephone)
The historical record indicates that Edison's approach was much more complex, that he made
use of available theories and resorted to trial and error only when no adequate theory existed
The method works ! Resulted in fascinating
compounds . Correlated electron materials do
“big things “ . Large volume collapses, ultra
strong magnets, heavy fermions, ………. ,
high temperature superconductivity ……
New phenomenal every few years……..
But the serendipity part is is a bit slow….
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Mean Field Theories Replace a many body problem by a
single site problem in an effective medium reference frame

- å J S S

i , j  ,
i, j
(tij   ij )(ci† c j  c†j ci )  U  ni ni
ij
i
j
- h å Si
i
H Anderson Imp   (V c0† A +c.c). 
 ,


,
i
  A A 


†
,
H MF = - heff So
 c0† c0  Uc0† c0 c0† c0
DMFT
Effective medium: quantifieds the
DMFT self consistency : medium
notion of “ metallicity” or itineracy to reproduce the exact (best ) local
spectral function of the problem.
A. Georges and G. Kotliar PRB 45, 6479 (1992).
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Phase diagram :frustrated Hubbard model, integer
filling M. Rozenberg G. Kotliar H. Kajuter G. Thomas PRL75, 105 (1995)
Mott transition
Coherence
Incoherence
Crossover
Transfer
of
spectral
weight
T/W
Quasiparticles
+Hubbard
bands
Spectral
functions
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M. Rozenberg G. Kotliar H. Kajueter G
Thomas D. Rapkine J Honig and P Metcalf
Phys. Rev. Lett. 75, 105 (1995)
T=170
High temperature universality
and V2O3
Mo, Denlinger, Kim, Park, Allen,
Sekiyama, Yamasaki, Kadono, Suga,
Saitoh, Muro, Metcalf, Keller, Held,
Eyert, Anisimov, Vollhardt PRL .
(2003)
T=300
P. Limelette
et.al.
Science
302,
89 (2003)
Critical
endpoint
Spinodal Uc2
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4f’s heavy fermions, 115’s, CeMIn5
M=Co, Ir, Rh
 CeRhIn5: TN=3.8 K;   450 mJ/molK2
 CeCoIn5: Tc=2.3 K;   1000 mJ/molK2;
 CeIrIn5: Tc=0.4 K;   750 mJ/molK2
Expts: F. P. Mena et.al, PRB 72, 045119 (2005).
K. S. Burch et al., PRB 75, 054523 (2007).
E. J. Singley, et, al PRB 65, 161101(R) (2002).
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Ir
In
Ce
Structure Property Relation: Ce115’s
Optics and Multiple hybridization gaps
non-f spectra
300K
eV
10K
J. Shim K Haule and
GK Science (2007)
In
Ce
In
•Larger gap due to hybridization with out of
plane In
•Smaller gap due to hybridization with inplane In
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Localization Delocalization in Actinides
Mott Transition
 Pu


Modern understanding of this phenomenaDMFT.
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DMFT Phonons in fcc -Pu
( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003)
(experiments from Wong et.al, Science, 22 August 2003)
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DMFT concept: Solids are Made out of Atoms.
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f shell in a medium . Valence Histogram
| 0 > ,|- > ,|¯> ,|- ¯>
®
| LSJM J g... >
Plutonium has an unusual
form of MIXED VALENCE
with clear spectral
fingerprints.
Shim, Khaule
Kotliar,
Nature, 446,
513-516
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(2007).
Photoemission
Havela et. al. Phys. Rev. B
68, 085101 (2003)
Pu is non magnetic – Cm is magnetic TN ~ 150 K.
K.Haule J. Shim and GK Nature 446, 513 (2007)
Cuprates : fundamental questions
•Relevant degrees of freedom ?
•Mechanism of the superconductivity ?
K>
-K>
•Quasiparticles glued by spin fluctuations,
•or condensation of RVB paired spins .
[ P. W. Anderson, Science 235, 1196 (1987)
•How to describe the underlying normal state ?
• Difference among different families
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Slave boson MFT.
G. Kotliar and J. Liu
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PRB 38,5412 (1988)
• D wave symmetry of the SC OP
•
SC order and Tc decrease as x
decreases.
• Low doping . pseudogap with D
wave symmetry .
b¹ 0
•VF is weakly dependent on doping, .
• Coherence incoherence crossover
on the overdoped side.
•
Related T=0 approach using wave functions:T. M. Rice
group. Zhang et. al. Supercond Scie Tech 1, 36 (1998,
Gross Joynt and Rice (1986) M. Randeria N. Trivedi , A.
Paramenkanti PRL 87, 217002 (2001)
D singlet pairing OP
b itineracy OP
Hubbard model : plaquette in a medium.
Lichtenstein and Kastnelson PRB (2000)
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Link DMFT. Normal state Real Space Picture. Ferrero
et. al. (2010) (similar to plaquette Haule and GK) (2006)
Singlet formation. S (singlet),T
(triplet) N=2 singlet, triplet
E (empty) N=0
1+ states with 1 electron in + orb
• Momentum Space Picture: High T
Underdoped region: arcs shrink as T is reduced. Overdoped
region FS sharpens as T is reduced.
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Reminiscent of PW
Anderson RVB
Science
235,
Superexchange
Mechanism?
. K.
Haule
and1196
GK(1987)
Phys.and
Rev.
boson picture
G. Kotliar and J. Liu P.RB 38,5412 (1988)
Bslave
76, 104509
(2007).
Ex= Jij(< Si. Sj >s- < Si . Sj>n)/t
How is the energy distributed
in q and w ?
D.J. Scalapino and S.R. White, Phys. Rev. B 58,
8222 (1998).
Expts; Dai et.al.
Building phase diagram
magnetization at T=0 vs .
Single site
Two site
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Origin of magnetism :Comparing the AF
and the “underlying PM state “
<EK>sdw -<EK>pm
 Unn  sdw   Unn  pm
Weber Haule and GK Nature Physics
10, 1038 (2010).
NCCO magnetizes to lower its
double occupancy ! Slater.
LSCO gains kinetic energy when it
magnetizes. [Mott ] NCCO pays kinetic
energy [Slater ]
Can be traced to the structure: absence of
apical oxygens reduces the charge transfer
energy
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Cuprates Superconductors
• Plaquette DMFT reasonable reference frame to
think about the qualitative physics of cuprates,
starting from high temperatures.
• High Tc materials. are near the single site DMFT
Mott boundary. LSCO more correlated than NCCO,
role of apical oxygens.
• High temperature superconductivity occurs in the
region where neither wave/itinerant nor localized/
particle picture fully applies. [ Alterantive viewpoint
to spin fluctuation theory ] , i.e. where perturbation
theory fails more catastrophically ( Murphy’s law).
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Realistic DMFT as a conceptual tool and a computational tool
DMFT (simple yet accurate ? ) reference frame to think about
electrons in solids and compute their properties.
Compare different “states” of the system for the same value of
parameters.  Understand Mechanism for ordering , magnetic,
superconducting, exotic, ……….
Bridge between atomic information and physical and
spectroscopical properties. [Structure-Property relation
Learning --> Design ? ]
Qualitative and quantitative system specific results gives us
confidence in the method. Many examples (sp, 3d,4d, 5d, 4f,
5f…)
New arenas Interfaces, junctions heterostructures, artificial
materials containing correlated electrons
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“Matthias’s Rules” for High Tc
• Metals. Must have d electrons (not just s s-p,
nor f). Stay away from oxides.
• High symmetry is good, cubic is best. Nb3Sn
• Certain electron concentrations are favored
(look for peak in density of states at Fermi
level)
• Stay away from theorists
• “ Do not follow my rules “
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Thanks!! for your attention!
$upport : NSF -DMR , DOE-Basic Energy Sciences, DOECMSN, AOSR - MURI, NSF-materials world network.
Reference: G. Kotliar, S. Savrasov, K. Haule, V. Oudovenko, O. Parcollet,
and C. Marianetti, Rev. Mod. Phys. 78, 000865 (2006)
C Marianetti
J. Shim
K. Haule
S. Savrasov
C. Weber