Band structure of strongly correlated materials from the Dynamical Mean Field perspective

1. K Haule Rutgers University Collaborators : J.H. Shim & Gabriel Kotliar Band structure of strongly correlated materials from the Dynamical Mean Field perspective

2. Dynamical Mean Field Theory in combination with band structure LDA+DMFT results for 115 materials (CeIrIn5) Local Ce 4f - spectra 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 Iron based superconductors and DMFT predictions Outline • References: • J.H. Shim, KH, and G. Kotliar, Science 318, 1618 (2007). • J.H. Shim, KH, and G. Kotliar, Nature 446, 513 (2007). • KH, J.H. Shim, and G. Kotliar, cond-mat/arXiv:0803.1279.

3. M. Van Schilfgarde 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

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.

5. New concepts, new techniques….. DMFT maybe the simplest approach to describe the physics of strong correlations -> the spectral weight transfer 1B HB model (DMFT): DMFT can describe Mott transition: Bright future!

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

7. D DMFT + electronic structure method 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).

8. high T low T DMFT is not a single impurity calculation Auxiliary impurity problem: temperature dependent: Weiss field High-temperature D given mostly by LDA low T: Impurity hybridization affected by the emerging coherence of the lattice (collective phenomena) DMFT SCC: Feedback effect on D makes the crossover from incoherent to coherent state very slow!

9. An exact impurity solver, continuous time QMC - expansion in terms of hybridization K.H. Phys. Rev. B 75, 155113 (2007) General impurity problem Diagrammatic expansion in terms of hybridization D +Metropolis sampling over the diagrams • Exact method: samples all diagrams! • Allows correct treatment of multiplets

10. Luttinger Ward functional NCA Same expansion using diagrammatics – real axis solver every atomic state represented with a unique pseudoparticle atomic eigenbase - full (atomic) base , where OCA general AIM: SUNCA ( )

11. How to computed 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 Basic questions to address

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

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

14. ? A(w) w k Issues for the system specific study • How does the crossover from localized moments • to itinerant q.p. happen? • How does the spectral • weight redistribute? • 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?

15. Temperature dependence of the localCe-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 up to very high • frequency J. H. Shim, KH, and G. Kotliar Science 318, 1618 (2007).

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

17. Anomalous Hall coefficient Consistency with the phenomenological approach of NPF Fraction of itinerant heavy fluid m* of the heavy fluid Remarkable agreement with Y. Yang & D. Pines Phys. Rev. Lett. 100, 096404 (2008).

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

19. 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

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

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

22. Momentum resolved total spectra A(w,k) 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 ARPES, HE I, 15K LDA+DMFT at 10K Fujimori, 2003 Large lifetime of HBs -> similar to LDA(f-core) rather than LDA or LDA+U

23. w k first mid-IR peak at 250 cm-1 CeCoIn5 Optical conductivity F.P. Mena & D.Van der Marel, 2005 Typical heavy fermion at low T: no visible Drude peak no sharp hybridization gap 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

24. 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

25. 10K In eV Ce In Multiple hybridization gaps non-f spectra 300K • Larger gap due to hybridization with out of plane In • Smaller gap due to hybridization with in-plane In

26. Localized 4f: LaRhIn5, CeRhIn5 Shishido et al. (2002) T decreasing Itinerant 4f : CeCoIn5, CeIrIn5 Haga et al. (2001) Fermi surfaces of CeM In5 within LDA How does the Fermi surface change with temperature?

27. Slight increase of the electron FS with decr T M X M G X X M M X Electron fermi surfaces at (z=0) LDA+DMFT (400 K) LDA LDA+DMFT (10 K) a2 a2

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

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

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

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

32. dHva freq. and effective mass 300K 10K 5K

33. Fe,Ni As,P La,Sm,Ce O Iron based high-Tc superconductors x~5-20% Smaller c Higher Tc • Y. Kamihara et.al., Tokyo, JACS • X.H. Chen, et.al., Beijing, cm/0803.3790 • G.F. Chen et.al., Beijing, cm/0803.3603 • Z.A. Ren et.al, Beijing, unpublished • 2D square lattice of Fe • Fe - magnetic moment • As-plays the role of O in cuprates

34. Kink in resistivity maybe SDW Specific heat consistent with nodes! Possibly d wave.. LaFxO1-xFeAs Y. Kamihara et.al., J. Am. Chem. Soc. XXXX, XXX (2008) A.S. Sefat. et.al., cond-mat/0803.2403

35. LaFxO1-xFeAs • Undoped compound: • Huge resistivity • Huge spin susceptibility • (  >> 100 bigger than in LSCO • 50 x Pauli) • Doped compound: • Large resistivity >> opt. dop. Cuprates • Spin susceptibility of an almost free spins • ~C/(T+120K) with C of S~1 Wilson’s ratio R~1 F0a small Y. Kamihara, J. Am. Chem. Soc. XXXX, XXX (2008)

36. x2-y2 60meV yz, xz 160meV z2 60meV xy LDA for LaOFeAs KH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 LDA DOS LDA: phonons-Tc<1K LDA: Mostly iron bands at EF (correlations important) 6 electrons in 5 Fe bands: Filling 6/10

37. Not a one band model: all 5 bands important (for J>0.3) DMFT for LaFxO1-xFeAs 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) Slater insulator Need to create a singlet out of spin and orbit

38. Electron pockets around M and A upon doping Optical conductivity of a bad metal No Drude peak DMFT for LaFxO1-xFeAs In LaOFeAs semiconducting gap is opening Large scattering rate at 116K 10% doping T=116 K

39. Conclusions • DMFT can describe crossover from local moment regime to heavy fermion state in heavy fermions. The crossover 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 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. • LaOFeAs is very bad metal within LDA+DMFT. With doping it becomes Fermi liquid with coherence temperature ~100K.

40. Thank you!

41. Localization – delocalization transitionin Lanthanides and Actinides Localized Delocalized

42. Electrical resistivity & specific heat Heavy ferm. in an element Itinerant closed shell Am J. C. Lashley et al. PRB 72 054416 (2005)

43. NO Magnetic moments in Pu! Pauli-like from melting to lowest T No curie Weiss up to 600K

44. Curium versus Plutonium nf=6 -> J=0 closed shell (j-j: 6 e- in 5/2 shell) (LS: L=3,S=3,J=0) One more electron in the f shell One hole in the f shell • Magnetic moments! (Curie-Weiss law at high T, • Orders antiferromagnetically at low T) • Small effective mass (small specific heat coefficient) • Large volume • No magnetic moments, • large mass • Large specific heat, • Many phases, small or large volume

45. Standard theory of solids: • DFT: • All Cm, Am, Pu are magnetic in LSDA/GGA LDA: Pu(m~5mB), Am (m~6mB) Cm (m~4mB) Exp: Pu (m=0), Am (m=0) Cm (m~7.9mB) • Non magnetic LDA/GGA predicts volume up to 30% off. • In atomic limit, Am non-magnetic, but Pu magnetic with spin ~5mB • Many proposals to explain why Pu is non magnetic: • Mixed level model (O. Eriksson, A.V. Balatsky, and J.M. Wills) (5f)4 conf. +1itt. • LDA+U, LDA+U+FLEX (Shick, Anisimov, Purovskii) (5f)6 conf. • Cannot account for anomalous transport and thermodynamics • Can LDA+DMFT account for anomalous properties of actinides? • Can it predict which material is magnetic and which is not?

46. Starting from magnetic solution, Curium develops antiferromagnetic long range order below Tc above Tc has large moment (~7.9mB close to LS coupling) Plutonium dynamically restores symmetry -> becomes paramagnetic J.H. Shim, K.H., G. Kotliar, Nature 446, 513 (2007).

47. Magnetization of Cm: Multiplet structure crucial for correct Tk in Pu (~800K) and reasonable Tc in Cm (~100K) Without F2,F4,F6: Curium comes out paramagnetic heavy fermion Plutonium weakly correlated metal

48. Fingerprint of atomic multiplets - splitting of Kondo peak Gouder , Havela PRB 2002, 2003

49. Photoemission and valence in Pu |ground state > = |a f5(spd)3>+ |b f6 (spd)2> approximate decomposition Af(w) f5<->f6 f6->f7 f5->f4

50. Pu partly f5 partly f6 Valence histograms Density matrix projected to the atomic eigenstates of the f-shell (Probability for atomic configurations) f electron fluctuates between these atomic states on the time scale t~h/Tk (femtoseconds) • Probabilities: • 5 electrons 80% • 6 electrons 20% • 4 electrons <1% One dominant atomic state – ground state of the atom J.H. Shim, K. Haule, G. Kotliar, Nature 446, 513 (2007).