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 Rice University Houston 22 st February 2011 Rice University Houston 22 st February 2011 1 “ Approximate practical methods of applying quantum mechanics should be developed which can lead to an explanation of the main features of complex atomic systems without too much computation” Paul Dirac (1929)

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

5. Probing Electronic Structure:Photoemission Probing Electronic Structure:Photoemission Probability of removing an electron and transfering energy  =Ei-Ef, and momentum k f(  ) A(  ) M 2  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 4

6. 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 5 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 5

7. 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. A. Georges and G. Kotliar PRB 45, 6479 (1992). DMFT self consistency condition DMFT Collective field describing the localization delocalization phenomena Can be sublattice dependent, spin dependent, etc.. … Hubbard Model 8

9. DMFT concept: Solids are Made out of Atoms. f shell in a medium. Valence Histogram f shell in a medium. Valence Histogram8

10. 9 DMFT concepts and tools in electronic structure. LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). DMFT Bands in a frequency dependent potential DMFT atom in a medium described Numerous technical advances in the implementations of these ideas, advanced impurity solvers, optimal definitions of projectors, advanced basis sets ……… APPROXIMATE COMPUTATION OF ALL OBSERVABLES, OPTICS PHOTOEMISSION, TRANSPORT, ETC.. STUDY POSSIBLE “STATES”

11. 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 16 Quasiparticles +Hubbard bands Transfer of spectral weight Mott transition Coherence Incoherence Crossover Spectral functions

12. Critical endpoint Spinodal Uc2 20 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

13.  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 out of plane in-plane Ce In Ir 21

14. At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) At 300K very broad Drude peak (e-e scattering, spd lifetime~0.1eV) At 10K: At 10K: very narrow Drude peak very narrow Drude peak First MI peak at 0.03eV~250cm -1 First MI peak at 0.03eV~250cm -1 Second MI peak at 0.07eV~600cm -1 Second MI peak at 0.07eV~600cm -1 Optical conductivity in LDA+DMFT Shim, HK Gotliar Science (2007) ‏ 22

15. 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 et. al. Science 23

16. Localization Delocalization in Actinides Mott Transition  Modern understanding of this phenomenaDMFT.  Pu  17

17. DMFT Phonons in fcc  -Pu ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et.al, Science, 22 August 2003) 18

18. Photoemission Photoemission Gouder, Havela PRB 2002, 2003 alpa->delta volume collapse transition F0=4,F2=6.1 19

19. What is the valence in the late actinides ? Plutonium has an unusual form of MIXED VALENCE Shim, KH, Kotliar, Nature, 446, 513-516 (2007). 20

20. Iron Arsenides superconductors: first round. LaO FeAs (2008) D. J Singh and M.H. Du Phys. Rev. Lett. 100, 237003 (2008). LDA. Weak correlations, itinerant magnet. First paper predicting shape of fermi surface. [ later verified expt]. Haule K, Shim J H and Kotliar G Phys. Rev. Lett. 100, 226402 (2008 ). Rule out phonon mechanism [ Tc< 1] “Bad Semi-Metal” (U< Uc2). M/M*~ Z ~0.2–0.3. Near localizaton-delocalization transition. Multi-orbital modelSpin-orbital mechanism for superconductivity. [ 4 ev window DMFT orbital ] Q.Si and E.Abrahams Phys. Rev. Lett. 101, 076401. (2008). Strong correlation picture, from analysis of experimental data, projected (t-J )model, important role of frustration [J1-J2 model] 10

21. Strength of correlations are due to Fe Hunds rule J not to Hubbard U. K. Haule and G. Kotliar cond-mat arXiv:0805.0722 K. Haule and G. Kotliar cond-mat arXiv:0805.0722 New Journal of Physics 11 (2009) 025021 Hunds (Correlated) Metals NOT doped Hunds (Correlated) Metals NOT doped Mott Hubbard Insulators LDA value U=5ev Fe Pnictides and Chalcogenides (and more generally, many 4d and 5d compounds) are fundamentally different from 3d Oxides. 11

22. Cutoff wc=3000cm -1 ~.3 ev M. M. Qazilbash, J. J. Hamlin,1 R. E. Baumbach Lijun Zhang, D. J. Singh, M. B. Maple, and D. N. Basov Nature Physics 5, 647 (2009). LDA+DMFT had predicted correlation effects m/m* ~.3 -.2 this WAS seen in OPTICS. 12

23. Evidence for weak correlations in experiments LDA+DMFT studies by other groups, V. Anisimov, A. Georges, chose other parameters so as to get weak correlations m*/m~ 1.6 2. (see however Liebsch Ishida Craco Laad) Large number of weak coupling studies predict s+- superconductivity, in good agreement with phenomenology. 13

24. BaFe2As2 optics. F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV., nd=6.2 Theory : Kutepov Haule Savrasov and GK PRB 82, 045105 (2010). Orbitals defined in a much larger energy window, 8 ev, Expt : M. M. Qazilbash et.al. Nature Physics 5, 647 (2009). Substantial Mass Renormalization with no sharp satellites in the XAS or core level photoemission spectra. Hunds metals differ from doped oxides: role of As Substantial Mass Renormalization with no sharp satellites in the XAS or core level photoemission spectra. Hunds metals differ from doped oxides: role of As 14

25. 15 Experiment: W. Z. Hu, et al, PRL 101, 257005 (2008). Nakajima, M. et al. Phys. Rev. B 81, 104528 (2010). LDA+DMFT Theory: Z. P. Yin, Khaule and G. Kotliar, Magnetism and charge dynamics in iron pnictide Nature Physics (2011) Published online 13 February 2011 Excellent agrement for moment. Experiments: 0.87 µ B LDA+DMFT: 0.9 µ B experimental crystal structure. experimental crystal structure. LSDA gives 2.1 µ B Good agreement at high energy Magnetic State LDA+DMFT BaFe2As2 LDA+DMFT BaFe2As2

26. Paglione and Greene Nature Physics 6, 645(2010) The “space of materials” The families The phase diagram

27. Correlation phase diagram and ordered moment of Hunds metals. Yin et al. 17

28. Cuprates : fundamental questions 18 Relevant degrees of freedom, and orbitals [ d x2-y2, px py, pz, d z2 ] Effective hamiltonians Mechanism of the superconductivity ? Mechanism of the superconductivity ? Quasiparticles glued by spin fluctuations, phonons, or condensation of RVB paired spins Weak vs strong Correlsations How to describe the underlying normal state which does not fit in the fermi liquid paradigm - reference system to describe experiments- quantum criticality –strongly coupled electron boson system ………… How to describe the underlying normal state which does not fit in the fermi liquid paradigm - reference system to describe experiments- quantum criticality –strongly coupled electron boson system ………… Difference among different familie Difference among different familie

29. Hubbard model : plaquette in a medium. Lichtenstein and Kastnelson PRB (2000) Lichtenstein and Kastnelson PRB (2000) 19

30. Link and plaquette DMFT. Normal state Real Space Picture. Ferrero et. al. (2010) Haule and GK (2006) Momentum Space Picture: High T Singlet formation. S,T N=2 singlet, triplet E 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. 20

31. 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

32. Building phase diagram magnetization at T=0 vs . Single site Two site 22 22

33. Optical Spectral Weights in LSCO and NCCO (up to 1.5 ev) Cedric Weber, Kristjan Haule, Gabriel Kotliar Nature Physics 10, 1038 (2010). Comanac et. al. Nature PhysicsNature Phys. 4, 287290 (2008). Nature Physics 10, 1038 (2010). Nature Physics 10, 1038 (2010). 24 23

34. 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

35. Structure Property Relation in Correlated Systems: c axis optics in YBCO. Compare with experiments C axis optical conductvity Spectra Structure

36. 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  Design] Qualitative and quantitative system specific results gives us confidence in the method. Qualitative and quantitative system specific results gives us confidence in the method. New arenas Interfaces, junctions heterostructures, artificial materials containing correlated electrons New arenas Interfaces, junctions heterostructures, artificial materials containing correlated electrons 32 25

37. Iron Pnictides and Chalcogenides as Hunds Semi-Metals. Correlated metals ( Z ~.2-.3) because of the Hunds J not Hubbard U Intermediate correlation strength no Hubbard bands FeBa2As2 Spin polarization increases with increasing energy scale. Orbital polarization decreases with decreasing energy scale. Important role of crystal fields in controlling the correlation strength. Both correlation strength (size of the fluctuating moment) and Fermi surface control the size of the magnetic moment. Good agreement with ARPES and optics. Predictions for anisotropy in these quantities in untweened samples.. 26

38. 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 temerature superconductivity near “coherence incoherence” crossover. [ Alterantive viewpoint to spin fluctuation theory ] 27

39. “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 “ 28

40. Materials processing historicall speaking was a craft. It became an experimental science at a later stage. Then theory started to play a supporting role with the advent of density functinoal theory. DMFT in 2010, is still in an early stage of development. DMFT concepts and algorithms significantly extended the theoretical capablities. It serves as a very primitive compass to guide us in journeys thru the vast space of possible materials. Combination of theory and experiment opens an exciting range of possiblities.29

41. Thanks!! for your attention! $upport : NSF -DMR, DOE-Basic Energy Sciences, MURI, materials world network. A. Kutepov Z. Yin K. Haule S. Savrasov C. Weber

45. arXiv:1009.0271 Theory : arXiv:1007.2867Theory : arXiv:1007.2867 Magnetism and Charge Dynamics in Iron Pnictides Z. P. Yin, K. Haule, G. KotliarZ. P. YinK. HauleG. Kotliar

46. 10/2/2015Zhiping Yin, Rutgers University 46 X’ Z Y’ X’ Z Y’ arXiv:1009.0271

47. QUALITATIVE INSIGHTS: a) Strongly Frequency Dependent Spin and Orbital Exchange Splitting b) Spin splitting large at high frequency. Orbital splitting large at low frequency. c) Qualitative difference between BaFe2As2 and Oxides. QUALITATIVE INSIGHTS: a) Strongly Frequency Dependent Spin and Orbital Exchange Splitting b) Spin splitting large at high frequency. Orbital splitting large at low frequency. c) Qualitative difference between BaFe2As2 and Oxides. Z. P. Yin, KH, G. Kotliar Nature Physics in press.

48. DOS and valence histogram There is transfer of spectral weight to high energies, spectral weight is conserved. But the DOS is featuresless no satellites, and resembles the LDA! Strong Correlations without Hubbard bands. Big difference between oxides and pnictides important role of As.

49. Evolution of the correlations in Hunds metals LDA LDA+DMFT Static Magnetic Moment is Determined by strength of correlatoins AND by the shape of the Fermi Surface

51. On First Principles Approaches to Materials Science Auguste Compte (1830). “ Every attempt to emply mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry “ Paul Dirac (1929) “The underlying laws necessary for the mathematical theory of the whole chemistry are thus completely known and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble “ “ Approximate practical methods of applying quantum mechanics should be developed which can lead to an explanation of the main features of complex atomic systems without too much computation”

52. “ …John Slater, already in 1953, was obsessed with what I have rudely called the Great Solid State Dream machine. He envisioned that the new electronic computer could be applied to the task of automatically providing the electronic structure of any desired solid; and he literally believed that he would have the answers to any conceivable question. The latter idea was wrongheaded; but the former has gradually become a reality with the rise of what is now known as LDA. It is not enough appreciated that Slater himself provided the key element in that method. “ In the Rise of Complexity 1953-2002, PW Anderson writes:

53. But there are many cases where it fails spectacularly: essentially all of the interesting class of substances with magnetic inner shell atoms, most of which exhibit what has been called the Mott Phenomenon- a dominance of the local repulsion among inner shell electrons. “…A new version of the Dream Machine has recently been invented which is quite successful in most of these cases-DMFT, dynamical mean field theory cooked up by Georges and Kotliar where the assumption of locality of the self energy in time is abandoned… “ Phil Anderson on the rise of complexity 1953-2002

54. Correlated electrons are not well described by either the itinerant (wave) picture, or the localized (particle) picture. Difficult non perturbative problem. Theoretical Approaches Correlated electrons are not well described by either the itinerant (wave) picture, or the localized (particle) picture. Difficult non perturbative problem. Theoretical Approaches Phenomenology Study of exactly soluble (by numerical and analytical means) 1-d Hamiltonians Approximate methods for models in 2d-3d Guessing effective low energy theories. Dynamical Mean Field Theory. [ Exact in the Metzner Vollhard limit of infinite dimensions – now can bridge between structure and property of materials ]

57. 12 Spectra=- Im G(k,  ) LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Lichtenstein and Katsnelson (1998) LDA++

58. Conceptual Underpinning Diagrams: PT in W and G. Introduce projector Gloc Wloc : Chitra and Kotliar Phys. Rev. B 62, 12715 (2000) and Phys. Rev.B (2001). : Chitra and Kotliar Phys. Rev. B 62, 12715 (2000) and Phys. Rev.B (2001).

59. GW self energy for Si Beyond GW Coordination Sphere Proof of Principle Implementation Full implementation in the context of a a one orbital lattice model. P Sun and G. Kotliar Phys. Rev. B 66, 85120 (2002). Propose GW+DMFT. P.Sun and GK PRL (2004). Test various levels of self consistencyin Gnonloc Pinonloc Test notion of locality in LMTO basis set in various materials. N. Zeyn S. Savrasov and G. Kotliar PRL 96, 226403, 2006 N Zeyn S. Savrasov and G. K PRL 96, 226403 (2006) Still, summing all diagramas with dynamical U and obtaining the GW starting point is extremely expensive. So this is still a point of principle rather than a practical tool.

60. Total energy is derived from a functional of the density and Gloc Total energy is derived from a functional of the density and Gloc CHARGE SELF CONSISTENT LDA+DMFT. S. Savrasov GK (2002) 12 LDA+DMFT as an approximation to the general scheme Recent calculations using B3LYP hybrid + DMFT for Ce2O3. D. Jacob K. Haule and GK EPL 84, 57009 (2008) U is parametrized in terms of Slater integrals F0 F2 F4 …. Savrasov, Kotliar, Abrahams, Nature ( 2001)

61. LDA+DMFT Self-Consistency loop [Savrasov Kotliar 2002] Derived from the functional. LDA+DMFT Self-Consistency loop [Savrasov Kotliar 2002] Derived from the functional. DMFT U E dc REVIEW : G. Kotliar S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet, C.A. Marianetti, RMP 78, 865 (2006).

62. Total Energy as a function of volume for Pu W (ev) vs (a.u. 27.2 ev) Savrasov, Kotliar, Abrahams, Nature ( 2001) Non magnetic correlated state of fcc Pu. N, Zein Following Aryasetiwan Imada Georges Kotliar Bierman and Lichtenstein. PRB 70 195104. (2004) Pu

63. DMFT Phonons in fcc  -Pu C 11 (GPa) C 11 (GPa) C 44 (GPa) C 44 (GPa) C 12 (GPa) C 12 (GPa) C'(GPa) C'(GPa)Theory 34.56 34.56 33.03 33.03 26.81 26.81 3.88 3.88 Experiment 36.28 36.28 33.59 33.59 26.73 26.73 4.78 4.78 ( Dai, Savrasov, Kotliar,Ledbetter, Migliori, Abrahams, Science, 9 May 2003) (experiments from Wong et.al, Science, 22 August 2003)

64. 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)

65. A. Georges and G. Kotliar PRB 45, 6479 (1992). DMFT self consistency condition DMFT Collective field describing the localization delocalization phenomena Hubbard Hubbard Green Green

67. Superexchange Mechanism. K. Haule and GK Phys. Rev. B 76, 104509 (2007). Compare “normal “ and SC state at the same tempearture! Superexchange Mechanism. K. Haule and GK Phys. Rev. B 76, 104509 (2007). Compare “normal “ and SC state at the same tempearture! 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) 31

69. Neutron spectroscopy with LDA+DMFT Theory : H. Park, K. Haule and GK Experiments: L Harriger H. Luo M. Liu T. Perring C Frost H. Ju M. Norman and Pengcheng Dai : arXiv:1011.3771

70. CUPRATES

71. Bath 12 Return to models, Hubbard, t-J Link DMFT Ferrero et. al. Europhys. Lett. 85, 57009 (2009) Stanescu and Phillips P RB,69, 245104 (2004). Plaquette DMFT: Lichtenstein and Kastnelson PRB (2000) T. Maier, et. al. 2001, Europhys. Lett. 56, 563. Sordi et.al.. arXiv:1002.2960 Sordi et.al.. arXiv:1002.2960 Civelli et. al. Phys. Rev. Lett. 100, 046402 (2008) Haule and Kotliar Phys. Rev. B 76, 104509 (2007) Kinetic Energy Exchan ge Energy Real Space Momentum Space 26

72. Early studies of plaquette and link DMFT of Hubbard Lichtenstein and Kastnelson PRB (2000) Stanescu, T. D., and P. Phillips, 2003, Phys. Rev. Lett. 91,017002. DCA in 2x2 Jarrell, M., T. Maier, et. al. 2001, Europhys. Lett. 56, 563. Lichtenstein and Kastnelson PRB (2000) Stanescu, T. D., and P. Phillips, 2003, Phys. Rev. Lett. 91,017002. DCA in 2x2 Jarrell, M., T. Maier, et. al. 2001, Europhys. Lett. 56, 563.

74. Electron and Hole Doped Cuprates : Similar but Yet Different, why? C. Weber et.al. Nature Physics 2010 NCCO : Robust AF Phase Comensurate Magnetism Lower Tc T^2 resistivity. Non monotonic angle dependence of SC order parameter ……… Review: Armitage Fournier Green (2009) Apical oxygen 18181818

75. DMFT studies of copper oxides Strength of correlations (as quantified by single site DMFT) the most fundamental difference between NCCO and LSCO compounds. NCCO (   c 2 )straddle the Zaanen Sawatsky Allen localization delocalization boundary. Traced to the absence of apical oxygen in NCCO (structure property relation). Good agreement with many experiments follow from a simple [ plaquette/link /site ] reference frame. Good agreement with many experiments follow from a simple [ plaquette/link /site ] reference frame. In general, better modeling with DMFT (more sites, more orbitals etc ) better results. In general, better modeling with DMFT (more sites, more orbitals etc ) better results. Power of mean field theory : comparing “normal “ and magnetic states, comparing “normal” and superconducting states Power of mean field theory : comparing “normal “ and magnetic states, comparing “normal” and superconducting states 25

77. Iron Pnictides

78. Iron Pnictides- Chalcogenides FeSe 1-0.08, (Tc=27K @ 1.48GPa), Mizuguchi et.al., arXiv: 0807.4315 (Fe++)(Se__)Ba++(Fe++)2(As---)2

79. PG Iron pnictides (electron, hole, isovalent doping) AFM: Antiferromagnetic metal SC: Superconductor T: Tetragonal O: Orthorombic hole electron isovalent Similarity/differences with cuprates

80. Basic Questions Relevant degreens of freedom, effective hamiltonians Strength of the correlations. Localized vs itinerant Fe d electrons Mechanism of the superconductivity and magnetism……. New arena to test the LDA+DMFT methodology [ with and without experimental informantion!]

81. Coherence Incoherence Crossover Coherence Incoherence Crossover Hubbard U is not the “relevant” parameter. The Hund’s coupling brings correlations! Specific heat within LDA+DMFT for LaO 1-0.1 F 0.1 FeAs at U=4eV LDA value For J=0 there is negligible mass enhancement at U~W! K. Haule and G. Kotliar cond-matK. Haule and G. Kotliar cond-mat arXiv:0805.0722 K. Haule and G. Kotliar cond-mat, LaO 1-0.1 F 0.1 FeAs n

82. wc=3000cm -1 ~..3 ev Nature Physics 5, 647 (2009) M. M. Qazilbash,1,, J. J. Hamlin,1 R. E. Baumbach,1 Lijun Zhang,2 D. J. Singh,2 M. B. Maple,1 and D. N. Basov1

83. Photoemission reveals now Z ~.3

84. Freq. dep. U matrix well parametrized by F0 F2 F4 F0 = 4:9 eV, F2 = 6:4 eV and F4 = 4:3 eV., nc=6.2 Z =1/2 for x2- y2 and z2, Z =1/3 f xz; yz zx orbitals. Z =1/2 for x2- y2 and z2, Z =1/3 f xz; yz zx orbitals.

85. F0 = 4:9 eV, F2 = 6:4 eV F4 = 4:3 eV., nc=6.2 Exp: W.Z. Hu et.al., PRL 101, 257005 (2008) LDA+DMFT calculations Kutepov Haule Savrasov and Kotliar PRB (2010). Mass renormalization = 3 without satellites

86. LDA+DMFT Magnetic moment.95 muB Expt 1 muB L EXPT: Hu, W. Z. et al. Phys. Rev. Lett. 101, 257005. (2008). EXPT: Nakajima, M. et al. Phys. Rev. B 81, 104528 (2010) Theory Yin et. al. (2010)

87. Origin of the anisotropy is electronic Optical features sharpen in the polarized spectra. Experimental predictions. Measurements underway ( not easy !)

88. Spin polarization of the frequency dependent self energy (real part). Frequency dependent exchange splitting. Large at high energies.

89. Orbital polarization of the frequency dependent hybridization Weiss field. Lives only at very low energies.

90. Magnetic Stripe Phase of the FeAs materials: new insights from LDA+DMFT Z. Yin K. Haule and GK [ in preparation] a) At low energies conductivity goes up. Rapid coherence crossover from an incoherent normal state compensates for a loss of carriers. Gain kinetic energy at very low energies! b)For intermediate  loss in carriers (kinetic energy ) Focus on changes of Neff( , T) at various energy scales  in going to the magnetic state.

91. Mass enhancement, plasma frequency Optical conductivity PRB 82, 045105 (2010) Exp: W.Z. Hu et.al., PRL 101, 257005 (2008). Plasma frequency: LDA ~ 2.6eV DMFT ~ 1.6eV Exp ~ 1.6eV Mass enhancement of Fe-5d bands m*/m LDA ~3 Interband peak ~ 0.6eV Drude weight U=5eV, J=0.7eV Theory : Fourth generation of LDA+DMFT methods and codes. Kutepov Haule Savrasov and Kotliar (2010). Mass renormalization without satellites !

92. Yin Haule and GK (2010). How well do we fare in the magnetic phase ?. Structure of Magnetic ordering correctly predicted by LSDA. LDA+DMFT is also OK in this respect. Structure of Magnetic ordering correctly predicted by LSDA. LDA+DMFT is also OK in this respect. Experiments: 0.87 µ B Ba122 LSDA: 1.76-2.2 µ B at experimental crystal geometry LSDA: 0.87 µ B, relaxed structure, As 0.1 angstrom away from experiments, bad DOS and wrong optics. LSDA+U: 0.87 µ B with U=-0.85 eV, slightly improved DOS and optics, but not in good agreement with experiments. LDA+DMFT: 0.87 µ B with U=5.0 and J=0.7 eV experimental crystal structure, excellent ARPES, optics, anisotropy

93. Eliminate the hybridization to the semicore states included in GW but not in LDA +DMFT by rescaling. Define a projector. Use the same projector in calculating the U’s that you will use in your DMFT calculation Go back to basics: U’s for DMFT. ( Kutepov et. al. building on the PT in G and W by R. Chitra and G. K) Rigorous Definition of the Hubbard U and the Weiss Field Delta in a Solid. Kutepov et.al (2010) Approximate Wloc and Piloc using Self Consistent GW. Kutepov et. al. 2010

94. DMFT Concepts and Tools in electronic structure Valence Histograms. Describes the history of the “atom” in the solid, multiplets! Weiss Weiss field, collective hybridizationfunction, quantifies the degree of localization Weiss Weiss field, collective hybridizationfunction, quantifies the degree of localization Functionals of density and spectra give total energies Local Self Energies and Correlated Bands Local Spectral Function

95. Correlation phase diagram and ordered moment of Hunds metals. Yin et al.

98. DMFT Concepts Valence Histograms. Describes the history of the “atom” in the solid, multiplets! Weiss Weiss field, collective hybridizationfunction, quantifies the degree of localization Weiss Weiss field, collective hybridizationfunction, quantifies the degree of localization Functionals of density and spectra give total energies Local Self Energies and Correlated Bands Local Spectral Function

99. Further extensions, clusters, GW+DMFT … Electronic Structure Meets DMFT LDA+DMFT V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). Lichtentsein and Katsnelson. PRB 57,6884 (1998). Almbladh et.al.(1999), Chitra and Kotliar (2000) (2001). Savrasov Kotliar and Abrahams (2001) Large Number of Groups and Many Compounds have been studied. Functional formulations, life without U

100. Conceptual Underpinning Diagrams: PT in W and G. Introduce projector Gloc Wloc : Chitra and Kotliar Phys. Rev. B 62, 12715 (2000) and Phys. Rev.B (2001). : Chitra and Kotliar Phys. Rev. B 62, 12715 (2000) and Phys. Rev.B (2001).

101. Determine energy density and  self consistently from extremizing a functional. Savrasov and Kotliar PRB 69, 245101, (2001) Full self consistent implementation Determine energy density and  self consistently from extremizing a functional. Savrasov and Kotliar PRB 69, 245101, (2001) Full self consistent implementation 9 Spectra=- Im G(k,  ) DMFT meets electronic structure. LDA+DMFT. V. Anisimov, A. Poteryaev, M. Korotin, A. Anokhin and G. Kotliar, J. Phys. Cond. Mat. 35, 7359 (1997). DMFT Bands in a frequency dependent potential DMFT atom in a medium described

102. Standard Model of Solid State Physics In many materials ( Cu, Au, …)electrons in solids behave as waves, quasiparticles [Sommerfeld Bloch]. Simple conceptual picture of excitations [Landau] Powerful computational tools Density functional theory, Kohn Sham. First order perturbation theory in the screened Coulomb interactions [GW ] [Hedin] 2

103. Henry Enhenreich in Electronic Structure for Materials Science, Science (1987) DMFT in 2010, is also in an early stage of development. DMFT concepts and algorithms serve as a very primitive compass to guide us in journeys thru the vast space of possible materials. 2

104. Early studies Hubbard model : plaquette in a medium. Lichtenstein and Kastnelson PRB (2000) Stanescu, T. D., and P. Phillips, 2003, Phys. Rev. Lett. 91,017002. DCA in 2x2 Jarrell, M., T. Maier, et. al. 2001, Europhys. Lett. 56, 563. Lichtenstein and Kastnelson PRB (2000) Stanescu, T. D., and P. Phillips, 2003, Phys. Rev. Lett. 91,017002. DCA in 2x2 Jarrell, M., T. Maier, et. al. 2001, Europhys. Lett. 56, 563. 20