Forming quasiparticles out of
local moments, the case of heavy
fermion CeIrIn5
K Haule
Rutgers University
Collaborators : J.H. Shim, S.Savrasov & Gabriel Kotliar
ICAM, Aspen 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
Aspen 2007
Standard 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,GW
Predictions:
M. Van Schilfgarde
•total energies,
•stability of crystal phases
•optical transitions
Aspen 2007
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.
Aspen 2007
Universality of the Mott transition
Crossover: bad insulator to bad metal
Critical point
First order MIT
V2O3
Ni2-xSex
k organics
1B HB model
(DMFT):
Aspen 2007
Basic questions



How to computed spectroscopic quantities (single particle s
pectra, optical conductivity phonon dispersion…) from first
principles?
How to relate various experiments into a unifying picture.
New concepts, new techniques….. DMFT maybe simplest ap
proach to meet this challenge
Aspen 2007
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 DMFT+electronic structure method (LDA or GW):
For less correlated bands (s,p): use LDA or GW
For correlated bands (f or d): add all local diagrams by solving QIM
(G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006).
Aspen 2007
Continuous time “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
k
Diagrammatic expansion in terms of hybridization D
+Metropolis sampling over the diagrams
•Exact method: samples all diagrams!
•Allows correct treatment of multiplets
Aspen 2007
Crystal structure of 115’s
Tetragonal crystal structure
Ir IrIn2 layer
In
Ce CeIn3 layer
IrIn2 layer
4 in plane In neighbors
Ce
In
8 out of plane in neighbors
In
Aspen 2007
Phase diagram of 115’s
Why CeIrIn5?
•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
Aspen 2007
Coherence crossover in experiment
ALM in DMFT
Schweitzer&
Czycholl,1991
Crossover scale ~50K
•High temperature
Ce-4f local moments
out of plane
in-plan
e
•Low temperature –
Itinerant heavy bands
Aspen 2007
Issues for the system specific study
•How does the crossover from localized moments
to itinerant q.p. happen?
?
•Where in momentum spac
e q.p. appear?
A(w)
•How does the spectral
weight redistribute?
w
k
•What is the momentum
dispersion of q.p.?
•How does the hybridization gap look like in momentum spa
ce?
Aspen 2007
Temperature dependence of the local Ce-4f spectra
•At 300K, only Hubbard bands
•At low T, very narrow q.p. peak
(width ~3meV)
•SO coupling splits q.p.: +-0.28eV
SO
•Redistribution of weight between the
q.p. and the upper Hubbard band
(e
Aspen 2007
Buildup of coherence
coherent spectral weight
Buildup of coherence in single impurity case
T
TK
Very slow crossover!
coherence pea
k
scattering rate
coherent spectral weight
Slow crossover more consistent with NP&F
T
T*
NP&F: Nakatsuji,Pines&Fisk, 2004
T*
Crossover around 50K
Aspen 2007
Angle integrated photoemission vs DMFT
Experimental resolution ~30meV,
theory predicts 3meV broad band
Surface sensitive at 122eV
ARPES
Fujimori, 2006
Aspen 2007
Angle integrated photoemission vs DMFT
Lower Hubbard band
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
ARPES
Fujimori, 2006
Aspen 2007
Momentum resolved Ce-4f spectra Af(w,k)
Hybridization gap Fingerprint of spd’s due to hybridization
q.p. band
SO
T=10K
scattering rate~100meV
T=300K
Not much weight
Aspen 2007
Quasiparticle bands
LDA bands
LDA bands DMFT qp bands
DMFT qp bands
three bands, Zj=5/2~1/200
Aspen 2007
Momentum resolved total spectra
Most of weight transferred into
the UHB
LDA+DMFT at 10K
A(w,k)
ARPES, HE I, 15K
LDA f-bands [-0.5eV, 0.8eV] almost
disappear, only In-p bands remain
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
Fujimori, 2003
Large lifetime of HBs -> similar to LDA(f-core)
rather than LDA or LDA+U
Aspen 2007
Optical conductivity
F.P. Mena & D.Van der Marel, 2005
Typical heavy fermion at low T:
no visible Drude peak
w
no sharp
hybridization gap
k
first mid-IR peak
at 250 cm-1
Narrow Drude peak (narrow q.p. band)
Hybridization gap
second mid IR peak
at 600 cm-1
CeCoIn5
Interband transitions across
hybridization gap -> mid IR peak
E.J. Singley & D.N Basov, 2002
Aspen 2007
Optical conductivity in LDA+DMFT
•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
Aspen 2007
Multiple hybridization gaps
eV
10K
non-f spectra
300K
In
Ce
In
•Larger gap due to hybridization with out of plane
In
•Smaller gap due to hybridization with in-plane In
Aspen 2007
Fermi surfaces of CeM In5
within LDA
Localized 4f:
LaRhIn5, CeRhIn5
Shishido et al. (2002)
Itinerant 4f :
CeCoIn5, CeIrIn5
Haga et al. (2001)
Aspen 2007
de Haas-van Alphen experiments
LDA (with f’s in valence) is reasonable for CeIrIn5
Experiment
LDA
Haga et al. (2001)
Aspen 2007
Fermi surface changes under
pressure in CeRhIn5
localized
itinerant
Shishido, (2005)




Fermi surface reconstruction at 2.34GPa
Sudden jump of dHva frequencies
Fermi surface is very similar on both sides,
slight increase of electron FS frequencies
Reconstruction happens at the point of
maximal Tc
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 F
At low T, they are included in the FS
Aspen 2007
Electron fermi surfaces at (z=0)
Slight decrease of th
e electron FS with T
LDA
M
X
M
X
G
X
M
X
M
a2
LDA+DMFT (10 K)
LDA+DMFT (400 K)
a2
Aspen 2007
Electron fermi surfaces at (z=p)
No a in DMFT!
No a in Experiment!
LDA
A
R
A
R
Z
R
A
R
A
Slight decrease of th
e electron FS with T
LDA+DMFT (10 K)
LDA+DMFT (400 K)
a3
a3
a
Aspen 2007
Electron fermi surfaces at (z=0)
Slight decrease of th
e electron FS with T
LDA+DMFT (10 K)
LDA
M
X
M
X
G
X
M
X
M
LDA+DMFT (400 K)
b1
b1
b2
b2
c
Aspen 2007
Electron fermi surfaces at (z=p)
No c in DMFT!
Slight decrease of th
No c in Experiment! e electron FS with T
LDA+DMFT (10 K)
LDA
A
R
A
R
Z
R
A
R
A
b2
LDA+DMFT (400 K)
b2
c
Aspen 2007
Hole fermi surfaces at z=0
Big change-> from small hole like
to large electron like
LDA+DMFT (10 K)
LDA
M
X
e1
M
g
X
G
X
M
X
M
LDA+DMFT (400 K)
h
g
h
Aspen 2007
Hole fermi surface at z=p
LDA
A
R
A
R
Z
R
A
R
A
LDA+DMFT (10 K)
LDA+DMFT (400 K)
No Fermi surfaces
Aspen 2007
Fermi surfaces
Increasing temperature from 10K to 300K:
 Gradual decrease of electron FS
Most of FS parts show similar trend
Big change might be expected in the G plane –
small hole like FS pockets (g,h) merge into
electron FS e1 (present in LDA-f-core but not in LDA)
Fermi surface a and c do not appear in DMFT results
Aspen 2007
Conclusions





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 pres
ence 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 increa
sing temperature. Hole pockets merge into e1 electron FS.
Aspen 2007
ARPES of CeIrIn5
Fujimori et al. (2006)
Aspen 2007
dHvA frequencies
Exp
LDA
DMFT
10K
4.53
b1
---
B2
6.116.59
a1
5.075.56
5.09
a2
4.53
4.08
3.80
a3
4.24
3.83
3.27
electron
Fermi surfaces
Aspen 2007
Ce 4f partial spectral functions
LDA+DMFT (10K)
LDA+DMFT (400K)
Blue lines : LDA bands
Aspen 2007