bishop’s lodge, santa fe 2007 modelling the localized to itinerant electronic transition in the...
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Bishop’s Lodge, Santa Fe 2007
Modelling the Localized to Itinerant Electronic Transition in the Heavy Fermion System CeIrIn5
K HauleRutgers University
Collaborators : J.H. Shim & Gabriel Kotliar
Santa Fe 2007
Outline
LDA+DMFT results for CeIrIn5 Local Ce 4f - spectra of CeIrIn5 and comparison to AIPES) Momentum resolved spectra and comparison to ARPES Optical conductivity Two hybridization gaps and its connection to optics Fermi surface in DMFT
J. H. Shim, KH, and G. Kotliar Science, November 1 2007; Science Express1149064
Santa Fe 2007
Standard theory of solidsStandard theory of solids
Band Theory: electrons as waves: Rigid band picture: En(k) versus k
Landau Fermi Liquid Theory applicable
Very powerful quantitative tools: LDA,LSDA,GWVery powerful quantitative tools: LDA,LSDA,GW
Predictions:
•total energies,
•stability of crystal phases
•optical transitions
M. Van SchilfgardeM. Van Schilfgarde
Santa Fe 2007
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.
Strong correlation – Strong correlation –
Standard theory failsStandard theory fails
Santa Fe 2007
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):
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Basic questions to addressBasic questions to address
How to computed spectroscopic quantities (single particle spectra, optical conductivity phonon dispersion…) from first principles?
How to relate various experiments into a unifying picture.
New concepts, new techniques….. DMFT maybe simplest approach to meet this challenge
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DMFT + electronic structure methodDMFT + electronic structure method
(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).
obtained by DFT
Ce(4f) obtained by “impurity solution”Includes the collective excitations of the system
Self-energy is local in localized basis,in eigenbasis it is momentum dependent!
all bands are affected: have lifetimefractional weight
Ce-f orbital
other “light” orbitals
hybridization
Dyson equation
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): add all local diagrams by solving QIM
Santa Fe 2007
“Bands” are not a good concept in DMFT!
Frequency dependent complex object instead of “bands”
lifetime effectsquasiparticle “band” does not carry weight 1
DMFTDMFT
Spectral function is a good concept
In FL regime:Hybridization:
at low energy q.p. hybridization becomes at high energy
In DMFT:
Santa Fe 2007
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:
Santa Fe 2007
Ce
In
Ir
CeIn
In
Crystal structure of 115’s
CeIn3 layer
IrIn2 layer
IrIn2 layer
Tetragonal crystal structure
4 in plane In neighbors
8 out of plane in neighbors
3.27au
3.3 au
Santa Fe 2007
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
Santa Fe 2007
•How does the crossover from localized moments to itinerant q.p. happen?
•How does the spectral
weight redistribute?
•How does the hybridization gap look like in momentum space?
?
k
A()
•Where in momentum space q.p. appear?
•What is the momentum dispersion of q.p.?
Issues for the system specific study
Santa Fe 2007
(e
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, November 1 2007; 1149064
Santa Fe 2007
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
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Consistency with the phenomenological approach of
NPF
Remarkable agreement with Y. Yang & D. Pines cond-mat/0711.0789!
+C
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ARPESFujimori, 2006
Angle integrated photoemission vs DMFT
Experimental resolution ~30meV, theory predicts 3meV broad band
Surface sensitive at 122eV
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Angle integrated photoemission vs DMFT
ARPESFujimori, 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
Santa Fe 2007
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
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DMFT qp bands
LDA bands LDA bands DMFT qp bands
Quasiparticle bands
three bands, Zj=5/2~1/200
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Momentum resolved total spectra A(,k)
Fujimori, 2003
LDA+DMFT at 10K ARPES, HE I, 15K
LDA f-bands [-0.5eV, 0.8eV] almostdisappear, only In-p bands remain
Most of weight transferred intothe UHB
Very heavy qp at Ef,hard to see in total spectra
Below -0.5eV: almost rigid downshift
Unlike in LDA+U, no new band at -2.5eV
Large lifetime of HBs -> similar to LDA(f-core)rather than LDA or LDA+U
Santa Fe 2007
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
Santa Fe 2007
•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
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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
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Fermi surfaces of CeM In5 within LDA
Localized 4f:LaRhIn5, CeRhIn5
Shishido et al. (2002)
Itinerant 4f :CeCoIn5, CeIrIn5
Haga et al. (2001)
Santa Fe 2007
de Haas-van Alphen experiments
LDA (with f’s in valence) is reasonable for CeIrIn5
Haga et al. (2001)
Experiment LDA
Santa Fe 2007
Fermi surface changes under pressure in CeRhIn5
Fermi surface reconstruction at 2.34GPa Sudden jump of dHva frequencies Fermi surface is very similar on both sides, sl
ight increase of electron FS frequencies Reconstruction happens at the point of maxim
al Tc
Shishido, (2005)localized itinerant
We can not yet address FS change with pressure
We can study FS change with Temperature -
At high T, Ce-4f electrons are excluded from the FSAt low T, they are included in the FS
Santa Fe 2007
Electron fermi surfaces at (z=0)
LDA+DMFT (10 K)LDA LDA+DMFT (400 K)
X M
X
XX
M
MM
2 2
Slight decrease of the electron
FS with T
Santa Fe 2007
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 decrease of the electron
FS with T
Santa Fe 2007
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 decrease of the electron
FS with T
Santa Fe 2007
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 decrease of the electron
FS with T
Santa Fe 2007
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
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Hole fermi surface at z=
R A
R
RR
A
AANo Fermi surfaces
LDA+DMFT (400 K)LDA+DMFT (10 K)LDA
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dHva freq. and effective mass
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Gradual decrease of electron FS
Most of FS parts show similar trend
Big change might be expected in the plane – small hole like FS pockets (g,h) merge into electron FS 1 (present in LDA-f-core but not in LDA)
Fermi surface a and c do not appear in DMFT results
Increasing temperature from 10K to 300K:
Fermi surfacesFermi surfaces
Santa Fe 2007
Crossover from local moment regime to heavy fermion state is very slow.
Width of heavy quasiparticle bands is predicted to be only ~3meV. We predict a set of three heavy bands with their dispersion.
Mid-IR peak of the optical conductivity 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
Fermi surface changes gradually with temperature and most of electron FS parts are only slightly decreases with increasing temperature. Hole pockets merge into 1 electron FS.
ConclusionsConclusions
Santa Fe 2007
ARPES of CeIrIn5
Fujimori et al. (2006)
Santa Fe 2007
•Ir atom is less correlated than Co or Rh (5d / 3d or 4d)
•CeIrIn5 is more itinerant(coherent) than Co (further away from QCP)
CeCoIn5 CeRhIn5 CeIrIn5
Tc[K] 2.3K 2.1K@p>1.5GPa
0.4K
Cv/T[mJ/molK^2] 300 50 750
Why CeIrIn5?
Phase diagram of 115’s
Santa Fe 2007
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
K.H. Phys. Rev. B 75, 155113 (2007)
Continuous time “QMC” impurity solver, expansion in terms of hybridization
Santa Fe 2007
Ce 4f partial spectral functions
LDA+DMFT (10K) LDA+DMFT (400K)
Blue lines : LDA bands