1. Bishop’s Lodge, Santa Fe 2007 Modelling the Localized to Itinerant Electronic Transition in the Heavy Fermion System CeIrIn 5 K Haule Rutgers University Collaborators : J.H. Shim & Gabriel Kotliar

2. Santa Fe 2007 Outline LDA+DMFT results for CeIrIn 5  Local Ce 4f - spectra of CeIrIn 5 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

3. Santa Fe 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: total energies, stability of crystal phases optical transitions M. Van Schilfgarde

4. 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 – Standard theory fails

5. Santa Fe 2007 V2O3V2O3 Ni 2-x Se x  organics Universality of the Mott transition First order MIT Critical point Crossover: bad insulator to bad metal 1B HB model (DMFT):

6. Santa Fe 2007 Basic questions to address 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

7. Santa Fe 2007 DMFT + 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 lifetime fractional 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 GW For correlated bands (f or d): add all local diagrams by solving QIM

8. Santa Fe 2007 “Bands” are not a good concept in DMFT! Frequency dependent complex object instead of “bands” lifetime effects quasiparticle “band” does not carry weight 1 DMFT Spectral function is a good concept In FL regime: Hybridization: at low energy q.p. hybridization becomes at high energy In DMFT:

9. 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:

10. Santa Fe 2007 Ce In Ir Ce In Crystal structure of 115’s CeIn 3 layer IrIn 2 layer Tetragonal crystal structure 4 in plane In neighbors 8 out of plane in neighbors 3.27au 3.3 au

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

12. 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

13. 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

14. Santa Fe 2007 Very slow crossover! T*T* Slow crossover pointed out by NPF 2004 Buildup of coherence in single impurity case TKTK coherent spectral weight T scattering rate coherence peak Buildup of coherence Crossover around 50K

15. Santa Fe 2007 Consistency with the phenomenological approach of NPF Remarkable agreement with Y. Yang & D. Pines cond-mat/0711.0789! +C

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

17. Santa Fe 2007 Angle integrated photoemission vs DMFT ARPES Fujimori, 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

18. Santa Fe 2007 T=10K T=300K scattering rate~100meVFingerprint of spd’s due to hybridization Not much weight q.p. bandSO Momentum resolved Ce-4f spectra Af(,k)Af(,k) Hybridization gap

19. Santa Fe 2007 DMFT qp bandsLDA bands DMFT qp bands Quasiparticle bands three bands, Z j=5/2 ~1/200

20. Santa Fe 2007 Momentum resolved total spectra A( ,k) Fujimori, 2003 LDA+DMFT at 10K ARPES, HE I, 15K LDA f-bands [-0.5eV, 0.8eV] almost disappear, only In-p bands remain Most of weight transferred into the 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

21. 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 CeCoIn 5 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 peak at 600 cm -1 first mid-IR peak at 250 cm -1

22. 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

23. Santa Fe 2007 Ce In Multiple hybridization gaps 300K eV 10K Larger gap due to hybridization with out of pla ne In Smaller gap due to hybridization with in-plane I n non-f spectra

24. Santa Fe 2007 Fermi surfaces of CeM In5 within LDA Localized 4f: LaRhIn5, CeRhIn5 Shishido et al. (2002) Itinerant 4f : CeCoIn5, CeIrIn5 Haga et al. (2001)

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

26. Santa Fe 2007 Fermi surface changes under pressure in CeRhIn 5  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 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 FS At low T, they are included in the FS

27. Santa Fe 2007 Electron fermi surfaces at (z=0) LDA+DMFT (10 K) LDA LDA+DMFT (400 K)  XM X X X M MM 22 22 Slight decrease of th e electron FS with T

28. Santa Fe 2007  RA R R R A AA 33 a 3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 th e electron FS with T

29. Santa Fe 2007 LDA+DMFT (10 K) LDA LDA+DMFT (400 K)  XM X X X M MM c 22 22 11 11 Electron fermi surfaces at (z=0) Slight decrease of th e electron FS with T

30. Santa Fe 2007  RA R R R A AA c 22 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 th e electron FS with T

31. Santa Fe 2007 LDA+DMFT (10 K) LDA LDA+DMFT (400 K)  XM X X X M MM g h Hole fermi surfaces at z=0 g h Big change-> from small hole like to large electron like 11

32. Santa Fe 2007 Hole fermi surface at z=   RA R R R A AA No Fermi surfaces LDA+DMFT (400 K) LDA+DMFT (10 K) LDA

33. Santa Fe 2007 dHva freq. and effective mass

34. Santa Fe 2007  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 surfaces

35. 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 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  1 electron FS. Conclusions

36. Santa Fe 2007 ARPES of CeIrIn 5 Fujimori et al. (2006)

37. Santa Fe 2007 Ir atom is less correlated than Co or Rh (5d / 3d or 4d) CeIrIn 5 is more itinerant(coherent) than Co (further away from QCP) CeCoIn 5 CeRhIn 5 CeIrIn 5 Tc[K]2.3K2.1K@p> 1.5GPa 0.4K C v /T[mJ/molK^2]30050750 Why CeIrIn 5 ? Phase diagram of 115’s

38. 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

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