1. 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

2. 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

3. 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
M. Van Schilfgarde
Predictions:
total energies,
stability of crystal phases
optical transitions
Aspen 2007

4. 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

5. Crossover: bad insulator to bad metal
Universality of the Mott transition
Crossover: bad insulator to bad metal
Critical point
First order MIT
Ni2-xSex
V2O3
k organics
1B HB model (DMFT):
Aspen 2007

6. Basic questions
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
Aspen 2007

7. 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

8. Continuous time “QMC” impurity solver,
expansion in terms of hybridization
K.H. Phys. Rev. B 75, (2007)
P. Werner, Phys. Rev. Lett. 97, (2006)
General impurity problem
Diagrammatic expansion in terms of hybridization D
+Metropolis sampling over the diagrams k
Exact method: samples all diagrams!
Allows correct treatment of multiplets
Aspen 2007

9. Crystal structure of 115’s
Tetragonal crystal structure Ce In Ir Ce In
IrIn2 layer
3.27au
4 in plane In neighbors
3.3 au
CeIn3 layer
IrIn2 layer
8 out of plane in neighbors
Aspen 2007

10. 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
0.4K
Cv/T[mJ/molK^2]
300 50
750
Aspen 2007

11. Coherence crossover in experiment
ALM in DMFT
Schweitzer&
Czycholl,1991
Crossover scale ~50K
High temperature
Ce-4f local moments
Low temperature –
Itinerant heavy bands
out of plane
in-plane
Aspen 2007

12. Issues for the system specific study
How does the crossover from localized moments
to itinerant q.p. happen? ?
How does the spectral
weight redistribute? k w
A(w)
Where in momentum space q.p. appear?
What is the momentum
dispersion of q.p.?
How does the hybridization gap look like in momentum space?
Aspen 2007

13. 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.: eV SO
Redistribution of weight between the
q.p. and the upper Hubbard band
Aspen 2007

14. Buildup of coherence Very slow crossover!
Buildup of coherence in single impurity case TK
coherent spectral weight T
Very slow crossover! T*
coherence peak
Slow crossover more consistent with NP&F T*
coherent spectral weight T
NP&F: Nakatsuji,Pines&Fisk, 2004
scattering rate
Crossover around 50K
Aspen 2007

15. Angle integrated photoemission vs DMFT
Experimental resolution ~30meV,
theory predicts 3meV broad band
Surface sensitive at 122eV
ARPES
Fujimori, 2006
Aspen 2007

16. Angle integrated photoemission vs DMFT
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
ARPES
Fujimori, 2006
Aspen 2007

17. Momentum resolved Ce-4f spectra Af(w,k)
Hybridization gap
Fingerprint of spd’s due to hybridization
q.p. band
scattering rate~100meV SO
T=10K
T=300K
Not much weight
Aspen 2007

18. Quasiparticle bands LDA bands DMFT qp bands LDA bands DMFT qp bands
three bands, Zj=5/2~1/200
Aspen 2007

19. Most of weight transferred into
Momentum resolved total spectra
A(w,k)
LDA+DMFT at 10K
ARPES, HE I, 15K
Most of weight transferred into
the UHB
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

20. Optical conductivity Typical heavy fermion at low T:
F.P. Mena & D.Van der Marel, 2005
Typical heavy fermion at low T:
first mid-IR peak
at 250 cm-1 k w
no visible Drude peak
no sharp
hybridization gap
CeCoIn5
Narrow Drude peak (narrow q.p. band)
Hybridization gap
second mid IR peak
at 600 cm-1
Interband transitions across
hybridization gap -> mid IR peak
E.J. Singley & D.N Basov, 2002
Aspen 2007

21. 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

22. Multiple hybridization gaps
non-f spectra eV
10K
300K Ce In
Larger gap due to hybridization with out of plane In
Smaller gap due to hybridization with in-plane In
Aspen 2007

23. 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

24. de Haas-van Alphen experiments
LDA (with f’s in valence) is reasonable for CeIrIn5
Experiment
LDA
Haga et al. (2001)
Aspen 2007

25. 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 FS
At low T, they are included in the FS
Aspen 2007

26. Electron fermi surfaces at (z=0)
Slight decrease of the electron FS with T
LDA
LDA+DMFT (10 K)
LDA+DMFT (400 K) a2 a2 G X M
Aspen 2007

27. Electron fermi surfaces at (z=p)
Slight decrease of the electron FS with T
No a in DMFT!
No a in Experiment!
LDA
LDA+DMFT (10 K)
LDA+DMFT (400 K) a3 a3 Z R A a
Aspen 2007

28. Slight decrease of the electron FS with T
Electron fermi surfaces at (z=0)
Slight decrease of the electron FS with T
LDA
LDA+DMFT (10 K)
LDA+DMFT (400 K) b1 G X M b1 b2 b2 c
Aspen 2007

29. Slight decrease of the electron FS with T
Electron fermi surfaces at (z=p)
No c in DMFT!
No c in Experiment!
Slight decrease of the electron FS with T
LDA
LDA+DMFT (10 K)
LDA+DMFT (400 K) Z R A b2 b2 c
Aspen 2007

30. Hole fermi surfaces at z=0
Big change-> from small hole like
to large electron like
LDA
LDA+DMFT (10 K)
LDA+DMFT (400 K) e1 G X M g h g h
Aspen 2007

31. Hole fermi surface at z=p
LDA+DMFT (400 K)
LDA
LDA+DMFT (10 K) Z R A
No Fermi surfaces
Aspen 2007

32. 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

33. 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 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 e1 electron FS.
Aspen 2007

34. ARPES of CeIrIn5
Fujimori et al. (2006)
Aspen 2007

35. dHvA frequencies Exp LDA DMFT 10K b1 --- B2 6.11-6.59 a1 5.07-5.56
5.09
4.53 a2
4.08
3.80 a3
4.24
3.83
3.27
electron
Fermi surfaces
Aspen 2007

36. Ce 4f partial spectral functions
LDA+DMFT (10K)
LDA+DMFT (400K)
Blue lines : LDA bands
Aspen 2007