1. Strongly Correlated Electron Materials: Some DMFT Concepts and Applications Strongly Correlated Electron Materials: Some DMFT Concepts and Applications Gabriel Kotliar and Center for Materials Theory 1 1 Colloquium University of Toronto Canada March 3rd 2011

2. “Standard Model of Solids “ Band Theory. Fermi Liquid Theory (Landau 1957). Density Functional Theory (Kohn Sham 1964) energy functional of the density. Reference Frame for Weakly Correlated Systems. Starting point for perturbation theory in the screened Coulomb interactions (Hedin 1965) Phys. Rev. Lett. 93, 126406 (2004). + [ - ] Many other properties can be computed, transport, optics, phonons, etc… 2

3. Cuprate Experimental Phase diagram Damascelli, Shen, Hussain, RMP 75, 473 (2003) Anomalously small conductivities 3

4. Anomalous resistivities C. Urano et. al. PRL 85, 1052 (2000) Sr2RuO4 4

5. Probing Electronic Structure:Photoemission Probing Electronic Structure:Photoemission  e Angle integrated spectra 6 A(k,  Many other spectroscopic tools to “see” correlated electrons ! b)Strong correlation: fermi liquid parameters can’t be evaluated in perturbation theory or fermi liquid theory does not work. a)Weak correlations 5

6. Shining light on correlated electrons. Optical conductivity. Failure of the Standard Model: Anomalous Spectral Weight Transfer Optical Conductivity Schlesinger t.al (1993) = Neff (T, )depends on T  Very Non local transfer of spectral weight in FeSi D. Van der Marel et.al (2005) [ 1 ev 800 cm-1] Weight does not recover up to 5 ev. 6 Other probes for correlated electrons X-rays, neutrons, electrons, the kitchen sink, theory ……….

7. How to Make Correlated materials ? Put open shell in a cage Oxygen transition metal ion Cage : e.g 6 oxygen atoms (octahedra) or other ligands/geometry Build crystal with this building block or build layers separated by spacers Transition metal (open shell ) Transition metal ions Rare earth ions Actinides Li x CoO2, Na x CoO2 Battery materials Thermoelectrics VO 2 Room temperature MIT La 1-x SrxMnO3 Colossal Magnetoresistance La 1-x Sr x CuO4 High temperature superconductor 7

8. How to find interesting correlated materials ? Serendipity An aptitude for making desirable discoveries by accident The Edisonian approach to innovation is characterized by trial and error discovery rather than a systematic theoretical approach. (e.g. carbon microphone, basis of telephone) + E disonian approach 6 The method works ! Resulted in fascinating compounds. Correlated electron materials do “big things “. Large volume collapses, ultra strong magnets, heavy fermions, ………., high temperature superconductivity …… New phenomenal every few years…….. The historical record indicates that Edison's approach was much more complex, that he made use of available theories and resorted to trial and error only when no adequate theory existed But the serendipity part is is a bit slow…. … 8

9. Mean Field Theories Replace a many body problem by a single site problem in an effective medium reference frame DMFT A. Georges and G. Kotliar PRB 45, 6479 (1992). DMFT self consistency : medium to reproduce the exact (best ) local spectral function of the problem. Effective medium: quantifieds the notion of “ metallicity” or itineracy 9

10. Phase diagram :frustrated Hubbard model, integer filling Phase diagram :frustrated Hubbard model, integer filling M. Rozenberg G. Kotliar H. Kajuter G. Thomas PRL75, 105 (1995) T/W 10 Quasiparticles +Hubbard bands Transfer of spectral weight Mott transition Coherence Incoherence Crossover Spectral functions

11. Critical endpoint Spinodal Uc2 11 P. Limelette et.al. Science 302, 89 (2003) 89 (2003)T=170T=300 M. Rozenberg G. Kotliar H. Kajueter G Thomas D. Rapkine J Honig and P Metcalf Phys. Rev. Lett. 75, 105 (1995) Mo, Denlinger, Kim, Park, Allen, Sekiyama, Yamasaki, Kadono, Suga, Saitoh, Muro, Metcalf, Keller, Held, Eyert, Anisimov, Vollhardt PRL. (2003 ) Mo, Denlinger, Kim, Park, Allen, Sekiyama, Yamasaki, Kadono, Suga, Saitoh, Muro, Metcalf, Keller, Held, Eyert, Anisimov, Vollhardt PRL. (2003 ) High temperature universality and V2O3

12.  CeRhIn5: TN=3.8 K;   450 mJ/molK2  CeCoIn5: Tc=2.3 K;   1000 mJ/molK2;  CeIrIn5: Tc=0.4 K;   750 mJ/molK2 4f’s heavy fermions, 115’s, CeMIn 5 M=Co, Ir, Rh Ce In Ir 12 Expts: F. P. Mena et.al, PRB 72, 045119 (2005). K. S. Burch et al., PRB 75, 054523 (2007). E. J. Singley, et, al PRB 65, 161101(R) (2002).

13. Ce In In Structure Property Relation: Ce115’s Optics and Multiple hybridization gaps 300K eV10K Larger gap due to hybridization with out of plane InLarger gap due to hybridization with out of plane In Smaller gap due to hybridization with in- plane InSmaller gap due to hybridization with in- plane In non-f spectra J. Shim K Haule and GK Science (2007) 13

14. Localization Delocalization in Actinides Mott Transition  Modern understanding of this phenomenaDMFT.  Pu  14

15. DMFT Phonons in fcc  -Pu ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et.al, Science, 22 August 2003) 15

16. DMFT concept: Solids are Made out of Atoms. f shell in a medium. Valence Histogram f shell in a medium. Valence Histogram8 Plutonium has an unusual form of MIXED VALENCE with clear spectral fingerprints. Shim, Khaule Kotliar, Nature, 446, 513-516 (2007). 16

17. Photoemission Photoemission Havela et. al. Phys. Rev. B 68, 085101 (2003) Havela et. al. Phys. Rev. B 68, 085101 (2003) Pu is non magnetic – Cm is magnetic TN ~ 150 K. K.Haule J. Shim and GK Nature 446, 513 (2007)

18. Cuprates : fundamental questions 17 Relevant degrees of freedom ? Relevant degrees of freedom ? Mechanism of the superconductivity ? Mechanism of the superconductivity ? Quasiparticles glued by spin fluctuations, Quasiparticles glued by spin fluctuations, or condensation of RVB paired spins. or condensation of RVB paired spins. [ P. W. Anderson, Science 235, 1196 (1987) How to describe the underlying normal state ? How to describe the underlying normal state ? Difference among different families Difference among different families K > -K>

19. Slave boson MFT. SC order and Tc decrease as x decreases. Low doping. pseudogap with D wave symmetry. D wave symmetry of the SC OP D wave symmetry of the SC OP V F is weakly dependent on doping,. V F is weakly dependent on doping,. Coherence incoherence crossover on the overdoped side. Coherence incoherence crossover on the overdoped side. G. Kotliar and J. Liu PRB 38,5412 (1988) Related T=0 approach using wave functions:T. M. Rice group. Zhang et. al. Supercond Scie Tech 1, 36 (1998, Gross Joynt and Rice (1986) M. Randeria N. Trivedi, A. Paramenkanti PRL 87, 217002 (2001)18

20. Hubbard model : plaquette in a medium. Lichtenstein and Kastnelson PRB (2000) Lichtenstein and Kastnelson PRB (2000) 21

21. Link DMFT. Normal state Real Space Picture. Ferrero et. al. (2010) (similar to plaquette Haule and GK) (2006) Momentum Space Picture: High T Singlet formation. S (singlet),T (triplet) N=2 singlet, triplet E (empty) N=0 1+ states with 1 electron in + orb Underdoped region: arcs shrink as T is reduced. Overdoped region FS sharpens as T is reduced. 21

22. Superexchange Mechanism?. K. Haule and GK Phys. Rev. B 76, 104509 (2007). Ex= J ij ( s - n )/t D.J. Scalapino and S.R. White, Phys. Rev. B 58, 8222 (1998). How is the energy distributed in q and w ? Reminiscent of PW Anderson RVB Science 235, 1196 (1987) and slave boson picture Reminiscent of PW Anderson RVB Science 235, 1196 (1987) and slave boson picture G. Kotliar and J. Liu P.RB 38,5412 (1988) Expts; Dai et.al. 22

23. Building phase diagram magnetization at T=0 vs . Single site Two site 20

24. Origin of magnetism :Comparing the AF and the “underlying PM state “ sdw - pm sdw - pm LSCO gains kinetic energy when it magnetizes. [Mott ] NCCO pays kinetic energy [Slater ] NCCO magnetizes to lower its double occupancy ! Slater. Can be traced to the structure: absence of apical oxygens reduces the charge transfer energy 24 Weber Haule and GK Nature Physics 10, 1038 (2010). Weber Haule and GK Nature Physics 10, 1038 (2010).Physics 10, 1038 (2010). Physics 10, 1038 (2010).

25. Cuprates Superconductors Plaquette DMFT reasonable reference frame to think about the qualitative physics of cuprates, starting from high temperatures. High Tc materials. are near the single site DMFT Mott boundary. LSCO more correlated than NCCO, role of apical oxygens. High temperature superconductivity occurs in the region where neither wave/itinerant nor localized/ particle picture fully applies. [ Alterantive viewpoint to spin fluctuation theory ], i.e. where perturbation theory fails more catastrophically ( Murphy’s law). 25

26. Realistic DMFT as a conceptual tool and a computational tool DMFT (simple yet accurate ? ) reference frame to think about electrons in solids and compute their properties. Compare different “states” of the system for the same value of parameters.  Understand Mechanism for ordering, magnetic, superconducting, exotic, ………. Bridge between atomic information and physical and spectroscopical properties. [Structure-Property relation  Learning --> Design ? ] Qualitative and quantitative system specific results gives us confidence in the method. Many examples (sp, 3d,4d, 5d, 4f, 5f…) Qualitative and quantitative system specific results gives us confidence in the method. Many examples (sp, 3d,4d, 5d, 4f, 5f…) New arenas Interfaces, junctions heterostructures, artificial materials containing correlated electrons New arenas Interfaces, junctions heterostructures, artificial materials containing correlated electrons 32 26

27. “Matthias’s Rules” for High Tc Metals. Must have d electrons (not just s s-p, nor f). Stay away from oxides. High symmetry is good, cubic is best. Nb3Sn Certain electron concentrations are favored (look for peak in density of states at Fermi level) Stay away from theorists “ Do not follow my rules “ 27

28. Thanks!! for your attention! $upport : NSF -DMR, DOE-Basic Energy Sciences, DOE- CMSN, AOSR - MURI, NSF-materials world network. K. Haule S. Savrasov C. Weber C Marianetti J. Shim Reference: G. Kotliar, S. Savrasov, K. Haule, V. Oudovenko, O. Parcollet, and C. Marianetti, Rev. Mod. Phys. 78, 000865 (2006)