Rutgers Colloquium, 2008
Predicting and Understanding Correlated Electron Materials: A Computational Approach
Kristjan Haule
Collaborators: J.H. Shim & G. Kotliar
Outline
Standard theory of solids (Landau Fermi liquid, Density Functional Theory)
Complex correlated matter -> standard theory fails LDA+DMFT and its strengths Detailed comparison of LDA+DMFT results with experiment
s for a heavy fermion material CeIrIn5 Local Ce 4f - spectra and comparison to AIPES) Momentum resolved spectra and comparison to ARPES Optical conductivity and its connection to hybridization gaps Fermi surface in DMFT Sensitivity to substitution of transition metal ion: difference between
CeIrIn5, CeCoIn5 and CeRhIn5
References:•KH, J.H. Shim, and G. Kotliar, Phys. Rev. Lett 100, 226402 (2008)•J.H. Shim, KH, and G. Kotliar, Science 318, 1618 (2007).•J.H. Shim, KH, and G. Kotliar, Nature 446, 513 (2007).
Standard theory of solids-Standard theory of solids-
Fermi liquid theoryFermi liquid theory
Excitation spectrum of a fermion system has the same structure as the
excitation spectrum of a perfect Fermi gas.
Lev Davidovich Landau
One to one correspondence between the interacting system and Fermi gas
Nobel laureate 1962Rigid band
Well defined quasiparticles->Rigid bands with long lifetime
fundamentals
Becomes quantitative/predictiveBecomes quantitative/predictive
Kohn-Hohenberg-Sham (1964):One-to-one mapping between the interacting system in the ground state and Kohn-Sham system of non-interacting particles.
M
KL
Band Theory: electrons as waves: Rigid band picture: En(k) versus k
Walter Kohn,Nobel laureate 1998
All “complexity” hidden in the XC functional
Standard theory at workStandard theory at work
Very powerful quantitative tools were developed: Very powerful quantitative tools were developed:
DFT(LDA,LSDA,GGA) ,GWDFT(LDA,LSDA,GGA) ,GW
Predictions:
•total energies,
•stability of crystal phases
•optical transitions
M. Van SchilfgardeM. Van Schilfgarde
Complex electronic matterComplex electronic matter
Transition metal oxides
Oxygen
transition metal ion
Cage of 6 oxygen atoms (octahedra)
Build a microscopic crystal with this building block
Transition metal insideTransition metal ions
Rare earth ions
Actinides
Oxygen
V
Metal insulator transitionMetal insulator transition
Manning T. D. & Parkin I. P. J. Mater. Chem. ,14. Article (2004). Above 29º reflects heat,
Coating – smart window
V: Mott metal-insulator tr. at room TN. F. Mott, PRB 11, 4383 (1975)
VO2
Oxygen
Mn
Hard disk deviceGiant magnetoresistance
Albert Fert and Peter GrünbergNobel Laureate 2007
Mn: Colossal magnetoresistanceS.W. Cheong et.al., Nature 399, 560 (1999)
Colossal magnetoresistanceColossal magnetoresistance
V: Mott metal-insulator tr. at room TN. F. Mott, PRB 11, 4383 (1975)
LaMnO3+doping+layering
Oxygen
Co
Electronic refrigeration
Co: Giant thermopowerY. Wang et.al., Nature 423, 425 (2003)
Giant thermopowerGiant thermopower
Mn: Colossal magnetoresistanceS.W. Cheong et.al., Nature 399, 560 (1999)
V: Mott metal-insulator tr. at room TN. F. Mott, PRB 11, 4383 (1975)
NaxCo2O4
Oxygen
Ni,Ru
Electronic Electronic crystallization/nematiccrystallization/nematic
Ni: Electronic crystallizationJ. Tranquada et.al., PRL 73, 1003 (1993)
Co: Giant thermopowerY. Wang et.al., Nature 423, 425 (2003)
Mn: Colossal magnetoresistanceS.W. Cheong et.al., Nature 399, 560 (1999)
Ru: Electronic nematicR.A. Borzi et.al., Science 315, 214 (2007)
V: Mott metal-insulator tr. at room TN. F. Mott, PRB 11, 4383 (1975)
Electronic crystal
La2NiO4.125
Oxygen
Cu
Ni: Electronic crystallizationJ. Tranquada et.al., PRL 73, 1003 (1993)
High temperature High temperature superconductivitysuperconductivity
Co: Giant thermopowerY. Wang et.al., Nature 423, 425 (2003)
Mn: Colossal magnetoresistanceS.W. Cheong et.al., Nature 399, 560 (1999)
Ru: Electronic nematicR.A. Borzi et.al., Science 315, 214 (2007)
Cu: High temperature superconductorBednorz&Muller, Z Phys. 64, 189(1986) Nobel Laureate 1987
V: Mott metal-insulator tr. at room TN. F. Mott, PRB 11, 4383 (1975)
layering+doping
SmFxO1-xFeAs x~0.2 d)
Tc=55K, cm/0803.3603
a=3.933A, c=8.4287A
PrFxO1-xFeAs c) Tc=52K, cm/0803.4283
a=3.985A, c=8.595A
CeFxO1-xFeAs b) Tc=41 K, cm/0803.3790
a=3.996A, c=8.648A
LaFxO1-xFeAs a) Tc=26 K,
JACS-2008
a=4.036A, c=8.739 A
La1-xSrxOFeAs Tc=25K, cm/0803.3021,
a=4.035A, c = 8.771AS
maller
c,
perf
ect
an
gle
a) Hosono et.a.., Tokyo, JACSb) X.H. Chen, et.al., Beijing,arXiv: 0803.3790c) Zhi-An Ren, Beijing, arXiv: 0803.4283d) Zhi-An Ren, Beijing, arXiv: 0804.2053.
Fe high temperature Fe high temperature superconductorssuperconductors
Fe
As
Tetrahedral cage (rather than octahedral)
CeCoIn5 CeRhIn5 CeIrIn5 PuCoG5
Tc[K] SC 2.3K N 3.8 K SC 0.4K 18.3K
Tcrossover ~50K ~50K ~50K ~370K
Cv/T[mJ/molK^2] 300 400 750 100
CeCoIn5 CeRhIn5CeIrIn5 CeCoIn5
CeXIn5
Ce
InX
CeIn
In
Heavy fermion materials (115)Heavy fermion materials (115)
Ce atom in cage of 12 In atoms
Properties can be tuned (substitution,pressure, magnetic field) between
•antiferromagnetism•superconductivity•quantum critical point
AFM
SCSC
AFM+SC
•Need for new methods and techniques which can deal with strong electronic correlations
Strong correlation – Strong correlation –
Standard theory of solids failsStandard theory of solids fails
•The electronic matter in these materials has tremendous potential for applications (large response to small stimuli, variety of responses,…)
•But it involves strong electronic interactions and has proved
extremely difficult to understand
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.
Coherent+incoherent spectra
Why does it fail?Why does it fail?
Rigid band
Bright future!Bright future!
New concepts, new techniques…..
1B HB model 1B HB model (DMFT):(DMFT):DMFT can describe Mott transition:
Dynamical Mean Field Theory the simplest approach which can describe the physics of strong correlations
->the spectral weight transfer->Mott transition->local moments and itinerant bands, heavy
quasiparticles
Weiss mean field theory for spin systemsExact in the limit of large z
Classical problem of spin ina magnetic field
Problem of a quantum impurity (atom in a fermionic band)
Space fluctuations are ignored, time fluctuations are treated exactly
DMFT in a Nutt shellDMFT in a Nutt shell
Dynamical mean field theory (DMFT) for the electronic problem
exact in the limit of large z
DMFT + electronic structure methodDMFT + electronic structure method
(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).
Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated orbitals (s,p): use LDA or GWFor correlated orbitals (f or d): add all local diagrams by solving QIM
DMFTmultiband&multiplets
OCA
SU
NC
A
NCALuttinger Ward functional
General impurity solvers: a diagrammatic real axis solver
Sum most important diagrams
General impurity problem
K.H., J Kroha & P. Woelfle, Phys. Rev. B 64, 155111 (2001)
General impurity problem
Diagrammatic expansion in terms of hybridization +Metropolis sampling over the diagrams
•Exact method: samples all diagrams!•Allows correct treatment of multiplets
K.H. Phys. Rev. B 75, 155113 (2007)
An exact impurity solver, continuous time QMC - expansion in terms of hybridization
K.H. Phys. Rev. B 75, 155113 (2007) ; P Werner, PRL (2007); N. Rubtsov PRB 72, 35122 (2005).
DMFT+LMTO package
http://www.physics.rutgers.edu/~haule/download.html
Database of materials
To be available at
Basic questions to addressBasic questions to address
How to compute spectroscopic quantities (single particle spectra, optical conductivity phonon dispersion…) from first principles?
How to relate various experiments into a unifying picture.
DMFT maybe simplest approach to meet this challenge for correlated materials
?
Issues in complex electronic matter
•Electronic properties are a strong function of temperature, pressure, doping
•Electronic states are developing in a nontrivial way in (,k) space (rigid band picture does not apply)
One example of a “heavy fermion” system, Ce-115’s:
•How does the crossover from localized moments to itinerant q.p. happen?
k
A()
•Where in momentum space q.p. appear and
how?
Crossover scale ~50K
in-plane
out of plane
•Low temperature – Itinerant heavy bands
•High temperature Ce-4f local moments
ALM in DMFTSchweitzer&Czycholl,1991
Coherence crossover in experiment
Temperature dependence of the local Ce-4f spectra
•At low T, very narrow q.p. peak (width ~3meV)
•SO coupling splits q.p.: +-0.28eV
•Redistribution of weight up to very high frequency
SO
•At 300K, only Hubbard bands
J. H. Shim, KH, and G. Kotliar Science 318, 1618 (2007).
CeIrIn5
A() – number of available states per energyA(k,) – number of available states
per momentum per energy ACe-4f()
Very slow crossover!
T*
Slow crossover pointed out by NPF 2004
Buildup of coherence in single impurity case
TK
cohere
nt
spect
ral
weig
ht
T scattering rate
coherence peak
Buildup of coherence
Crossover around 50K
Remarkable agreement with Y. Yang & D. Pines Phys. Rev. Lett. 100, 096404 (2008).
Anom
alo
us
Hall
coeffi
cient
Fraction of itinerant heavy fluid
m* of the heavy fluid
Consistency with the phenomenological approach of NPF
+const
ARPESFujimori, 2006
Angle integrated photoemission vs DMFT
Experiment at T=10K
Maybe surface sensitive at 122eV
Angle integrated photoemission vs DMFT
ARPESFujimori, Phys. Rev. B 73, 224517 (2006).
Nice agreement for the• Hubbard band position•SO split qp peak
Hard to see narrow resonance
in ARPES since very little weight
of q.p. is below Ef
Lower Hubbard band
T=10K T=300Kscattering rate~100meV
Fingerprint of spd’s due to hybridization
Not much weight
q.p. bandSO
Momentum resolved Ce-4f spectraAf(,k)
Hybridization gap
CeIn
In
Optical conductivity
Typical heavy fermion at low T:
Narrow Drude peak (narrow q.p. band)
Hybridization gap
k
Interband transitions across hybridization gap -> mid IR peak
CeCoIn5
no visible Drude peak
no sharp hybridization gap
F.P. Mena & D.Van der Marel, 2005
E.J. Singley & D.N Basov, 2002
second mid IR peakat 600 cm-1
first mid-IR peakat 250 cm-1
•At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) •At 10K:
•very narrow Drude peak•First MI peak at 0.03eV~250cm-1
•Second MI peak at 0.07eV~600cm-1
Optical conductivity in LDA+DMFT
CeIn
In
Multiple hybridization gaps
300K
e V
10K
•Larger gap due to hybridization with out of plane In•Smaller gap due to hybridization with in-plane In
non-f spectra
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
X M
X
XX
M
MM
g h
Fermi surface change with T
g h
Big change-> from small hole like to large electron like
1
Difference between Co,Rh,Ir 115’s
more localizedmore itinerantIr Co Rh
superconducting magnetically ordered“good” Fermi liquid
Total and f DOS f DOS
CeIn
In
X
•Commensurate AFM stable below ~3K•Moment has mainly
7
symmetry: moment lies in the ab
plane•Moment is ~1B
In exp:• AFM stable below 3.8K, but is spiral
Q=(1/2,1/2,0.298)a
•For B>3T, Q=(1/2,1/2,1/4)b
•Moment in plane!•Moment 0.26a,b, 0.59b, 0.75c B , 0.79 B
d
CeRhIn5 is most localized -> susceptible to long range magnetic order
a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000)b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007)c) Bao W et al, Phys. Rev. B 62 R14621 (2000)d) J. Thompson & T. Park, (2008)
Magnetism in CeRhIn5
Complex correlated matter holds a great promise for future technological materials
There is a lack of tools for describing complex correlated matter from first principles
Many aspect of complex matter physics are well described by DMFT
We have shown one such example: heavy fermion materials CeXIn5 Temperature crossover Spectral weight redistribution in momentum and
frequency Sensitivity to chemical substitution
ConclusionsConclusions
Thank you!
Iron superconductors, structure
Fe,Ni
As,P
La,Sm,Ce
O•2D square lattice of Fe•Fe - magnetic moment•As-similar then O in cuprates
But As not in plane!
Fe
As
Perfect tetrahedra 109.47°
Phonons give Tc<1KKH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)):
What is the glue?
L. Boeri, O. V. Dolgov, A. A. Golubov arXiv:0803.2703(PRL, 101, 026403 (2008)):
<0.21, Tc<0.8K
Y. Kamihara et.al.,
J. Am. Chem. Soc. 130, 3296 (2008).
Kink in resistivity
Not conventional superconductors!
Huge spin susceptibility (50 x Pauli)
Signatures of moments
Susceptibility 50xlarger than Pauli LDAT. Nomura et.al., 0804.3569
Doped LaOFeAsCaFe2As2 and Ca0.5Na0.5Fe2As2
Large restivity in normal state
Importance of Hund’s couplingHubbard U is not the “relevant” parameter.
The Hund’s coupling brings correlations!
Specific heat within LDA+DMFTfor LaO1-0.1F0.1FeAs at U=4eV
LDA value
For J=0 there is negligible mass enhancement at U~W!J~0.35 gives correct order ofMagnitude for both and The coupling between the Fe magnetic moment and the mean-field medium
(As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling!KH, G. Kotliar, cond/mat 0803.1279
LaO1-0.1F0.1FeAs
Common features of the parent c.
CaFe2As2 and Ca0.5Na0.5Fe2As2SmOFeAs
Structural transition & SDW
superconductivity
Enormous normal state resistivities!Very unusual
Structural transitionSDW not noticed
superconductivity
Variety of materials
CaFe2As2, (Tc=12K @ 5.5GPa), Milton S. Torikachvili, arXiv:0807.0616v2
Li1-xFeAs, (Tc=18K), X.C.Wang et.al., arXiv:0806.4688
FeAs layer
Ba or Ca
(Ba1-xKx)Fe2As2 (Tc=38K, x~0.4), Marianne Rotter et.al., arXiv:0805.4630
hole doped (not electron doped)
FeSe1-0.08, (Tc=27K @ 1.48GPa), Yoshikazu Mizuguchi et.al., arXiv: 0807.4315
No arsenic !
A. Kreyssig, arXiv:0807.3032
Bond angle seems to matter most. Perfect tetrahedra (109.47° ) -> higher Tc
R O1-xFx FeAs electron doped
BaFeAs2 (Tc=?)J.H. Shim, KH, G. Kotliar, arXiv: 0809.0041
S.C. Riggs et.al., arXiv: 0806.4011
SmFeAsO1-xFx
Phase diagrams SmFeAsO
A. J. Drew et.al., arXiv:0807.4876.
muon spin rotation magneto-transport experiments
Very similar to cuprates, log(T) insulator due to impurities
A. Kreyssig et.al, arXiv: 0807.3032
CaFe2As2 under pressure
Phase diagrams CaFe2As2
Volume collapse
Stoichiometric compound
Common features of the parent c.
CaFe2As2 and Ca0.5Na0.5Fe2As2SmOFeAs
Structural transition & SDW
superconductivity
Enormous normal state resistivities!Very unusual
Structural transitionSDW not noticed
superconductivity
Magnetic and structural PT
LaOFeAs
R. Klingeler et.al., arXiv:0808.0708v1
Clarina de la Cruz, Nature 453, 899 (2008).
In single crystals of 122 seems TM and TS close or the same
Tetragonal->Orth.
magnetic
arXiv:0806.3304v1
Fe magnetism ?Weak structural distortion ~150 K: from tetragonal to orthorombic
SDW (stripe AFM) at lower T Neutrons by: Clarina de la Cruz et.al, Nature 453, 899 (2008). top view
side view
But Iron Fe2+ has 6 electrons, [Ar] 3d6 4s0 and spin S=2.
Why is not μ larger?Why it varies so much?
LaFeAsO: TSDW~140K μ~0.3-0.4μB (a)
NdFeAsO: TSDW~1.96K μ~0.9μB/Fe (b)
(c) Huang, Q. et al., arXiv:0806.2776
SDW temperature and magnetic moment vary strongly between compounds:
(b) Jan-Willem G. Bo, et.al., arXiv:0806.1450
(a) Clarina de la Cruz et.al, Nature 453, 899 (2008).
BaFe2As2: T0~TSDW~100K μ~0.9μB/Fe (c)
SrFe2As2: T0~TSDW~205K μ~1.01μB/Fe (d)
(d) K. Kaneko et.al., arXiv: 0807.2608
Itinerancy & Frustration
Magnetic exchange interaction is very frustrated (Qimiao Si, Elihu Abrahams, arXiv:0804.2480)
For the doped compound, LDA structural optimization fails for non-magnetic state! (It is very good if magnetism is assumed)
For non-magnetic state, LDA predicts 1.34Å shorter FeAs distance (10.39 instead of 11.73).One of the largest failures of LDA.
T. Yildirim, arXiv: 0807.3936
The undoped compound is metal (although very bad one ~1mcm), hence moment is partially screened
Exchange interactions are such that J2~J1/2, very strong frustration,(KH, G. Kotliar, arXiv: 0805.0722)
Paramagnetic statemust have (fluctuating)magnetic momentsnot captured in LDA
Signatures of moments
Susceptibility 50xlarger than Pauli LDAT. Nomura et.al., 0804.3569
Doped LaOFeAs
Band structure of LaOFeAs
LDA: Mostly iron bands at EF (correlations important)
6 electrons in 5 Fe bands:Filling 6/10 -> large spin
LDA DOS
KH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)):
The 5-band Hubbard-type modelAs(p)-Fe(d) hybridization weak
Hoppings available at http://www.physics.rutgers.edu/~haule/FeAs/
LDA+DMFT: LaOFeAs is at the verge of the metal-insulator transition (for realistic U=4eV, J=0.7eV)For a larger (U=4.5, J=0.7eV) semiconducing insulator
Not a one band model: all 5 bands important (for J>0.3)
Need to create a singlet out of spin and orbit
DMFT for LaFxO1-xFeAs
Importance of Hund’s couplingHubbard U is not the “relevant” parameter.
The Hund’s coupling brings correlations!
Specific heat within LDA+DMFTfor LaO1-0.1F0.1FeAs at U=4eV
LDA value
For J=0 there is negligible mass enhancement at U~W!J~0.35 gives correct order ofMagnitude for both and The coupling between the Fe magnetic moment and the mean-field medium
(As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling!KH, G. Kotliar, cond/mat 0803.1279
LaO1-0.1F0.1FeAs
DMFT can describe crossover from local moment regime to heavy fermion state in heavy fermions. The crossover is very slow.
Mid-IR peak of the optical conductivity in 115’s is split due to presence of two type’s of hybridization
Ce moment is more coupled to out-of-plane In then in-plane In which explains the sensitivity of 115’s to substitution of transition metal ion
Fermi surface in CeIrIn5 is gradually increasing with decreasing temperature but it is not saturated even at 5K.
The out-of plane impurity hybridization (at 7K) is for 50% larger in CeIrIn5 than in CeRhIn5.
CeIrIn5 is most itinerant and CeRhIn5 most localized.
ConclusionsConclusions
Fermi surfaces of CeM In5 within LDA
Localized 4f:LaRhIn5, CeRhIn5
Shishido et al. (2002)
Itinerant 4f :CeCoIn5, CeIrIn5
Haga et al. (2001)
T decreasing
How does the Fermi surface change with temperature?
Electron fermi surfaces at (z=0)
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
X M
X
XX
M
MM
2 2
Slight increase of the
electron FS with decr T
R A
R
RR
A
AA
3
a
3
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
Electron fermi surfaces at (z=)No a in DMFT!No a in Experiment!
Slight increase of the
electron FS with decr T
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
X M
X
XX
M
MM
c
2 2
11
Electron fermi surfaces at (z=0)Slight increase of the electron FS
with decr T
R A
R
RR
A
AA
c
2 2
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
Electron fermi surfaces at (z=)No c in DMFT!No c in Experiment!
Slight increase of the electron FS
with decr T
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
X M
X
XX
M
MM
g h
Hole fermi surfaces at z=0
g h
Big change-> from small hole like to large electron like
1
Difference between Co,Rh,Ir 115’s
more localizedmore itinerantIr Co Rh
superconducting magnetically ordered“good” Fermi liquid
Total and f DOS f DOS
Mean field hybridization of Ce 4f electrons
in space:
the angular part:
at low frequency – we diagonalize:
The three important terms:
The origin of the difference: hybridization
In-plane hybridizationis small
•Ir largest,•Co next•Rh smallest
Out of-plane hybridizationIs large, difference important
•Ir largest•Co next•Rh much smaller
The distance to in-plane and out-of plane In is almost the same
In2
In1
Out-of plane hyb.very weak in Rh
Vanishing optical Hybridization gap!
more localizedmore itinerantIr Co Rh
superconducting magnetically ordered
“good” Fermi liquid
Distance between Ce and in-plane In:6.246 6.164 6.222
Distance between Ce and out-of-plane In:6.183 6.202 6.194
Angle 45° -0.59° 45° +0.35° 45° -0.26°
In(2): (1,0,1-0.02030)x4.4164 (1,0,1+0.01246)x4.3586 (1,0,1-0.00894)x4.3994
Distance of Ce-In(1,2)?
angleAngle=45°: In(1) and In(2) are at the same distance from Ce
It is not the structure, but the ion itself, that makes the difference!Difference between Co/Rh/Ir atom and not the structure is relevant.
The structure difference is the secondary effect.
•Commensurate AFM stable below ~3K•Moment has mainly
7
symmetry: moment lies in the ab
plane•Moment is ~1B
In exp:• AFM stable below 3.8K, but is spiral
Q=(1/2,1/2,0.298)a
•For B>3T, Q=(1/2,1/2,1/4)b
•Moment 0.26a,b, 0.59b, 0.75c B , 0.79 Bd
Magnetism in CeRhIn5
CeRhIn5 is most localized -> susceptible to long range magnetic order
a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000)b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007)c) Bao W et al, Phys. Rev. B 62 R14621 (2000)d) J. Thompson & T. Park, (2008)
Fe,Ni
As,P
La,Sm,Ce
O
SmFeAsO1-xFx
New Iron high-Tc’sThursday 14. August, afternoon (2:30-…)
Frequency dependence of hybridization
Substantial differenceCoherence scale exponentially sensitive to hybridization
Relative importance of atomic states
N=1N=0
Probability to find electron in one of the atomic states (CeIrIn5)
most important
20% lower p.
10% less
empty 10% less
Magnetism in CeRhIn5
CeRhIn5 shows a clear signature of a Kondo peak above TNell
Kondo screening relatively poor compared to other two 115’sNell state develops out of partly localized/itinerant state
Fujimori 2006Rh has a small hump
dHva freq. and effective mass
300K
10K5K
DMFT is not a single impurity calculation
Auxiliary impurity problem:
High-temperature given mostly by LDA
low T: Impurity hybridization affected by the emerging coherence of the lattice
(collective phenomena)
Weiss field temperature dependent:
Feedback effect on makes the crossover from incoherent to coherent state very slow!
high T
low T
DMFT SCC:
Nonmagnetic impurities not detrimental to SC
BaFe1.8Co0.2As2: Tc~22K
•Fe replaced by Co •Impurities do not destroy SC (like Zn doping in cuprates)•No signature of Curie-Weiss susc.
F.L. Ning et.al, arXiv:0808.1420
V2O3Ni2-xSex organics
Universality of the Mott transitionUniversality of the Mott transition
First order MITCritical point
Crossover: bad insulator to bad metal
1B HB model 1B HB model (DMFT):(DMFT): B
ad in
sula
tor
Bad metal1B HB model 1B HB model (plaquette):(plaquette):
DMFT for a simple systemDMFT for a simple system
Identify correspondence between the local and impurity quantities:
Identify correspondence between the local and full GF:
Solve QIM:
Equivalent to summation of all local Feynman diagramsA. Georges & G. Kotliar, RMP 1996
Iron SC: How it all started….
Published in Chemical journal (Journal of American Chemical Society)Received January 2008, published online Feb 2008
And exploded….more than 23 cond-mat’s in March 2008
>260 preprints at the end of July mostly from China!
R=(0,0) R=(1,0)
R=(1,1)
Reference systemsReference systems
Reference system in DFT: Kohn-Sham system of independent electrons
Reference system in DMFT: One interacting atom + system of independent electronsInteracting cluster+ system of independent electrons
Kohn-Sham: Potential is local and static
Self-energy is short ranged and retarded
Obtained by solving a QIM