1. Rutgers Colloquium, 2008 Predicting and Understanding Correlated Electron Materials: A Computational Approach Kristjan Haule Collaborators: J.H. Shim & G. Kotliar

2. Outline  Standard theory of solids (Landau Fermi liquid, Density Functional Theory)  Complex correlated matter -> standard theory fails  LDA+DMFT and its strengths  Detailed comparison of LDA+DMFT results with experiments for a heavy fermion material CeIrIn 5 Local Ce 4f - spectra and comparison to AIPES) Momentum resolved spectra and comparison to ARPES Optical conductivity and its connection to hybridization gaps Fermi surface in DMFT Sensitivity to substitution of transition metal ion: difference between CeIrIn5, CeCoIn5 and CeRhIn5 References: KH, J.H. Shim, and G. Kotliar, Phys. Rev. Lett 100, 226402 (2008) J.H. Shim, KH, and G. Kotliar, Science 318, 1618 (2007). J.H. Shim, KH, and G. Kotliar, Nature 446, 513 (2007).

3. Standard theory of solids- Fermi liquid theory Excitation spectrum of a fermion system has the same structure as the excitation spectrum of a perfect Fermi gas. Lev Davidovich Landau One to one correspondence between the interacting system and Fermi gas Nobel laureate 1962 Rigid band Well defined quasiparticles-> Rigid bands with long lifetime fundamentals

4. Becomes quantitative/predictive Kohn-Hohenberg-Sham (1964): One-to-one mapping between the interacting system in the ground state and Kohn-Sham system of non-interacting particles.mapping M K L Band Theory: electrons as waves: Rigid band picture: En(k) versus k Walter Kohn, Nobel laureate 1998 All “complexity” hidden in the XC functional

5. Standard theory at work Very powerful quantitative tools were developed: DFT(LDA,LSDA,GGA),GW Predictions: total energies, stability of crystal phases optical transitions M. Van Schilfgarde

6. Complex electronic matter Transition metal oxides Oxygen transition metal ion Cage of 6 oxygen atoms (octahedra) Build a microscopic crystal with this building block Transition metal inside Transition metal ions Rare earth ions Actinides

7. Oxygen V Metal insulator transition Manning T. D. & Parkin I. P. J. Mater. Chem.,14. Article (2004). Above 29º reflects heat, Coating – smart window V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) VO 2

8. Oxygen Mn Hard disk device Giant magnetoresistance Albert Fert and Peter Grünberg Nobel Laureate 2007 Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature 399, 560 (1999) Colossal magnetoresistance V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) LaMnO 3 +doping+layering

9. Oxygen Co Electronic refrigeration Co: Giant thermopower Y. Wang et.al., Nature 423, 425 (2003) Giant thermopower Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature 399, 560 (1999) V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Na x Co 2 O 4

10. Oxygen Ni,Ru Electronic crystallization/nematic Ni: Electronic crystallization J. Tranquada et.al., PRL 73, 1003 (1993) Co: Giant thermopower Y. Wang et.al., Nature 423, 425 (2003) Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature 399, 560 (1999) Ru: Electronic nematic R.A. Borzi et.al., Science 315, 214 (2007) V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) Electronic crystal La 2 NiO 4.125

11. Oxygen Cu Ni: Electronic crystallization J. Tranquada et.al., PRL 73, 1003 (1993) High temperature superconductivity Co: Giant thermopower Y. Wang et.al., Nature 423, 425 (2003) Mn: Colossal magnetoresistance S.W. Cheong et.al., Nature 399, 560 (1999) Ru: Electronic nematic R.A. Borzi et.al., Science 315, 214 (2007) Cu: High temperature superconductor Bednorz&Muller, Z Phys. 64, 189(1986) Nobel Laureate 1987 V: Mott metal-insulator tr. at room T N. F. Mott, PRB 11, 4383 (1975) layering+doping

12. SmF x O 1-x FeAs x~0.2 d) Tc=55K, cm/0803.3603 a=3.933A, c=8.4287A PrF x O 1-x FeAs c) Tc=52K, cm/0803.4283 a=3.985A, c=8.595A CeF x O 1-x FeAs b) Tc=41 K, cm/0803.3790 a=3.996A, c=8.648A LaF x O 1-x FeAs a) Tc=26 K, JACS-2008 a=4.036A, c=8.739 A La 1-x Sr x OFeAs Tc=25K, cm/0803.3021, a=4.035A, c = 8.771A Smaller c, perfect ang le a)Hosono et.a.., Tokyo, JACS b)X.H. Chen, et.al., Beijing,arXiv: 0803.3790 c)Zhi-An Ren, Beijing, arXiv: 0803.4283 d)Zhi-An Ren, Beijing, arXiv: 0804.2053. Fe high temperature superconductors Fe As Tetrahedral cage (rather than octahedral)

13. CeCoIn 5 CeRhIn 5 CeIrIn 5 PuCoG 5 Tc[K]SC 2.3KN 3.8 KSC 0.4K18.3K T crossover ~50K ~370K C v /T[mJ/molK^2]300400750100 CeCoIn 5 CeRhIn 5 CeIrIn 5 CeCoIn 5 CeXIn 5 Ce In X Ce In Heavy fermion materials (115) Ce atom in cage of 12 In atoms Properties can be tuned (substitution, pressure, magnetic field) between antiferromagnetism superconductivity quantum critical point AFM SC AFM+SC

14. Need for new methods and techniques which can deal with strong electronic correlations Strong correlation – Standard theory of solids fails The electronic matter in these materials has tremendous potential for applications (large response to small stimuli, variety of responses,…) But it involves strong electronic interactions and has proved extremely difficult to understand

15. 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. Coherent+incoherent spectra Why does it fail? Rigid band

16. Bright future! New concepts, new techniques….. 1B HB model (DMFT): DMFT can describe Mott transition: Dynamical Mean Field Theory the simplest approach which can describe the physics of strong correlations ->the spectral weight transfer ->Mott transition ->local moments and itinerant bands, heavy quasiparticles

17. Weiss mean field theory for spin systems Exact in the limit of large z Classical problem of spin in a magnetic field Problem of a quantum impurity (atom in a fermionic band) Space fluctuations are ignored, time fluctuations are treated exactly DMFT in a Nutt shell Dynamical mean field theory (DMFT) for the electronic problem exact in the limit of large z

18. DMFT + electronic structure method (G. Kotliar S. Savrasov K.H., V. Oudovenko O. Parcollet and C. Marianetti, RMP 2006). Basic idea of DMFT+electronic structure method (LDA or GW): For less correlated orbitals (s,p): use LDA or GW For correlated orbitals (f or d): add all local diagrams by solving QIM  DMFT multiband& multiplets

19. OCA SUNCA NCA Luttinger Ward functional General impurity solvers: a diagrammatic real axis solver Sum most important diagrams General impurity problem K.H., J Kroha & P. Woelfle, Phys. Rev. B 64, 155111 (2001)

20. 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.H. Phys. Rev. B 75, 155113 (2007) An exact impurity solver, continuous time QMC - expansion in terms of hybridization K.H. Phys. Rev. B 75, 155113 (2007) ; P Werner, PRL (2007); N. Rubtsov PRB 72, 35122 (2005).

21. DMFT+LMTO package http://www.physics.rutgers.edu/~haule/download.html Database of materials To be available at

22. Basic questions to address How to compute spectroscopic quantities (single particle spe ctra, optical conductivity phonon dispersion…) from first pri nciples? How to relate various experiments into a unifying picture. DMFT maybe simplest approach to meet this challenge for correlated materials

23. ? Issues in complex electronic matter Electronic properties are a strong function of temperature, pressure, doping Electronic states are developing in a nontrivial way in ( ,k) space (rigid band picture does not apply) One example of a “heavy fermion” system, Ce-115’s: How does the crossover from localized moments to itinerant q.p. happen? k  A(  ) Where in momentum space q.p. appear and how?

24. 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

25. 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 318, 1618 (2007). CeIrIn 5 A(  ) – number of available states per energy A(k,  ) – number of available states per momentum per energy A Ce-4f (  )

26. 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

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

28. ARPES Fujimori, 2006 Angle integrated photoemission vs DMFT Experiment at T=10K Maybe surface sensitive at 122eV

29. Angle integrated photoemission vs DMFT ARPES Fujimori, Phys. Rev. B 73, 224517 (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

30. 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 Ce In

31. 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

32. 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

33. 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

34. LDA+DMFT (10 K) LDA LDA+DMFT (400 K)  XM X X X M MM g h Fermi surface change with T g h Big change-> from small hole like to large electron like 11

35. Difference between Co,Rh,Ir 115’s more localized more itinerant Ir Co Rh superconducting magnetically ordered “good” Fermi liquid Total and f DOS f DOS Ce In X

36. Commensurate AFM stable below ~3K Moment has mainly   7 symmetry: moment lies in the ab plane Moment is ~1  B In exp: AFM stable below 3.8K, but is spiral Q=(1/2,1/2,0.298) a For B>3T, Q=(1/2,1/2,1/4) b Moment in plane! Moment 0.26 a,b, 0.59 b, 0.75 c  B, 0.79  B d CeRhIn 5 is most localized -> susceptible to long range magnetic order a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000) b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007) c) Bao W et al, Phys. Rev. B 62 R14621 (2000) d) J. Thompson & T. Park, (2008) Magnetism in CeRhIn 5

37. Complex correlated matter holds a great promise for future technological materials There is a lack of tools for describing complex correlated matter from first principles Many aspect of complex matter physics are well described by DMFT We have shown one such example: heavy fermion materials CeXIn5  Temperature crossover  Spectral weight redistribution in momentum and frequency  Sensitivity to chemical substitution Conclusions

38. Thank you!

39. Iron superconductors, structure Fe, Ni As, P La,Sm,Ce O 2D square lattice of Fe Fe - magnetic moment As-similar then O in cuprates But As not in plane! Fe As Perfect tetrahedra 109.47°

40. Phonons give Tc<1K KH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)): What is the glue? L. Boeri, O. V. Dolgov, A. A. Golubov arXiv:0803.2703 (PRL, 101, 026403 (2008)): <0.21, Tc<0.8K Y. Kamihara et.al., J. Am. Chem. Soc. 130, 3296 (2008). Kink in resistivity Not conventional superconductors! Huge spin susceptibility (50 x Pauli)

41. Signatures of moments Susceptibility 50xlarger than Pauli LDA T. Nomura et.al., 0804.3569 Doped LaOFeAs CaFe 2 As 2 and Ca 0.5 Na 0.5 Fe 2 As 2 Large restivity in normal state

42. Importance of Hund’s coupling 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! J~0.35 gives correct order of Magnitude for both  and  The coupling between the Fe magnetic moment and the mean-field medium (As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling! KH, G. Kotliar, cond/mat 0803.1279 LaO 1-0.1 F 0.1 FeAs

43. Common features of the parent c. CaFe 2 As 2 and Ca 0.5 Na 0.5 Fe 2 As 2 SmOFeAs Structural transition & SDW superconductivity Enormous normal state resistivities! Very unusual Structural transition SDW not noticed superconductivity

44. Variety of materials CaFe 2 As 2, (Tc=12K @ 5.5GPa), Milton S. Torikachvili, arXiv:0807.0616v2 Li 1-x FeAs, (Tc=18K), X.C.Wang et.al., arXiv:0806.4688 FeAs layer Ba or Ca (Ba 1-x K x )Fe 2 As 2 (Tc=38K, x~0.4), Marianne Rotter et.al., arXiv:0805.4630 hole doped (not electron doped) FeSe 1-0.08, (Tc=27K @ 1.48GPa), Yoshikazu Mizuguchi et.al., arXiv: 0807.4315 No arsenic ! A. Kreyssig, arXiv:0807.3032arXiv:0807.3032 Bond angle seems to matter most. Perfect tetrahedra (109.47° ) -> higher Tc R O 1-x F x FeAs electron doped BaFeAs 2 (Tc=?) J.H. Shim, KH, G. Kotliar, arXiv: 0809.0041

45. S.C. RiggsS.C. Riggs et.al., arXiv: 0806.4011 SmFeAsO 1-x F x Phase diagrams SmFeAsO A. J. DrewA. J. Drew et.al., arXiv:0807.4876.arXiv:0807.4876 muon spin rotation magneto-transport experiments Very similar to cuprates, log(T) insulator due to impurities

46. A. KreyssigA. Kreyssig et.al, arXiv: 0807.3032 CaFe 2 As 2 under pressure Phase diagrams CaFe 2 As 2 Volume collapse Stoichiometric compound

47. Common features of the parent c. CaFe 2 As 2 and Ca 0.5 Na 0.5 Fe 2 As 2 SmOFeAs Structural transition & SDW superconductivity Enormous normal state resistivities! Very unusual Structural transition SDW not noticed superconductivity

48. Magnetic and structural PT LaOFeAs R. Klingeler et.al., arXiv:0808.0708v1arXiv:0808.0708v1 Clarina de la Cruz, Nature 453, 899 (2008). In single crystals of 122 seems T M and T S close or the same Tetragonal->Orth. magnetic arXiv:0806.3304v1

49. Fe magnetism ? Weak structural distortion ~150 K: from tetragonal to orthorombic SDW (stripe AFM) at lower T Neutrons by: Clarina de la Cruz et.al, Nature 453, 899 (2008). top view side view But Iron Fe 2+ has 6 electrons, [Ar] 3d6 4s0 and spin S=2. Why is not μ larger? Why it varies so much? LaFeAsO: T SDW ~140K μ~0.3-0.4μB (a) NdFeAsO: T SDW ~1.96K μ~0.9μB/Fe (b) (c) Huang, Q. et al., arXiv:0806.2776 SDW temperature and magnetic moment vary strongly between compounds: (b) Jan-Willem G. Bo, et.al., arXiv:0806.1450 (a) Clarina de la Cruz et.al, Nature 453, 899 (2008). BaFe 2 As 2 : T 0 ~T SDW ~100K μ~0.9μB/Fe (c) SrFe 2 As 2 : T 0 ~T SDW ~205K μ~1.01μB/Fe (d) (d) K. Kaneko et.al., arXiv: 0807.2608

50. Itinerancy & Frustration Magnetic exchange interaction is very frustrated (Qimiao Si, Elihu Abrahams, arXiv:0804.2480) For the doped compound, LDA structural optimization fails for non-magnetic state! (It is very good if magnetism is assumed) For non-magnetic state, LDA predicts 1.34Å shorter FeAs distance (10.39 instead of 11.73). One of the largest failures of LDA. T. Yildirim, arXiv: 0807.3936 The undoped compound is metal (although very bad one ~1m  cm), hence moment is partially screened Exchange interactions are such that J2~J1/2, very strong frustration, (KH, G. Kotliar, arXiv: 0805.0722) Paramagnetic state must have (fluctuating) magnetic moments not captured in LDA

51. Signatures of moments Susceptibility 50xlarger than Pauli LDA T. Nomura et.al., 0804.3569 Doped LaOFeAs

52. Band structure of LaOFeAs LDA: Mostly iron bands at EF (correlations important) 6 electrons in 5 Fe bands: Filling 6/10 -> large spin LDA DOS KH, J.H. Shim, G. Kotliar, cond/mat 0803.1279 (PRL. 100, 226402 (2008)): The 5-band Hubbard-type model As(p)-Fe(d) hybridization weak Hoppings available at http://www.physics.rutgers.edu/~haule/FeAs/

53. 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) semiconducing insulator Not a one band model: all 5 bands important (for J>0.3) Need to create a singlet out of spin and orbit DMFT for LaF x O 1-x FeAs

54. Importance of Hund’s coupling 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! J~0.35 gives correct order of Magnitude for both  and  The coupling between the Fe magnetic moment and the mean-field medium (As-p,neighbors Fe-d) becomes ferromagnetic for large Hund’s coupling! KH, G. Kotliar, cond/mat 0803.1279 LaO 1-0.1 F 0.1 FeAs

55. DMFT can describe crossover from local moment regime to heavy fermion state in heavy fermions. The crossover is very slow. Mid-IR peak of the optical conductivity in 115’s is split due to pr esence 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 tr ansition metal ion Fermi surface in CeIrIn5 is gradually increasing with decre asing temperature but it is not saturated even at 5K. The out-of plane impurity hybridization (at 7K) is for 50% l arger in CeIrIn5 than in CeRhIn5. CeIrIn5 is most itinerant and CeRhIn5 most localized. Conclusions

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

57. 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 increase of the electron FS with decr T

58.  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 increase of the electron FS with decr T

59. 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 increase of the electron FS with decr T

60.  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 increase of the el ectron FS with decr T

61. 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

62. Difference between Co,Rh,Ir 115’s more localized more itinerant Ir Co Rh superconducting magnetically ordered “good” Fermi liquid Total and f DOS f DOS

63. Mean field hybridization of Ce 4f electrons in space: the angular part: at low frequency – we diagonalize: The three important terms:

64. The origin of the difference: hybridization    In-plane hybridization is small Ir largest, Co next Rh smallest Out of-plane hybridization Is large, difference important Ir largest Co next Rh much smaller The distance to in-plane and out-of plane In is almost the same In 2 In 1 Out-of plane hyb. very weak in Rh Vanishing optical Hybridization gap!

65. more localized more itinerant Ir Co Rh superconducting magnetically ordered “good” Fermi liquid Distance between Ce and in-plane In: 6.246 6.164 6.222 Distance between Ce and out-of-plane In: 6.183 6.202 6.194 Angle 45° -0.59° 45° +0.35° 45° -0.26° In(2): (1,0,1-0.02030)x4.4164 (1,0,1+0.01246)x4.3586 (1,0,1-0.00894)x4.3994 Distance of Ce-In(1,2)? angle Angle=45°: In(1) and In(2) are at the same distance from Ce It is not the structure, but the ion itself, that makes the difference! Difference between Co/Rh/Ir atom and not the structure is relevant. The structure difference is the secondary effect.

66. Commensurate AFM stable below ~3K Moment has mainly   7 symmetry: moment lies in the ab plane Moment is ~1  B In exp: AFM stable below 3.8K, but is spiral Q=(1/2,1/2,0.298) a For B>3T, Q=(1/2,1/2,1/4) b Moment 0.26 a,b, 0.59 b, 0.75 c  B, 0.79  B d Magnetism in CeRhIn 5 CeRhIn 5 is most localized -> susceptible to long range magnetic order a) Wei Bao, P. G. Pagliuso, J. L. Sarrao, J. D. Thompson, and Z. Fisk, Phys. Rev. B 62, R14 621 (2000) b) S Raymond, E Ressouche, G Knebel, D Aoki and J Flouquet, J. Phys.: Condens. Matter 19 (2007) c) Bao W et al, Phys. Rev. B 62 R14621 (2000) d) J. Thompson & T. Park, (2008)

67. Fe, Ni As, P La,Sm,Ce O SmFeAsO 1-x F x New Iron high-Tc’s Thursday 14. August, afternoon (2:30-…)

68. Frequency dependence of hybridization Substantial difference Coherence scale exponentially sensitive to hybridization

69. Relative importance of atomic states N=1 N=0 Probability to find electron in one of the atomic states (CeIrIn5)     most important     20% lower p.    10% less empty 10% less

70. Magnetism in CeRhIn 5 CeRhIn 5 shows a clear signature of a Kondo peak above T Nell Kondo screening relatively poor compared to other two 115’s Nell state develops out of partly localized/itinerant state Fujimori 2006 Rh has a small hump

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

73. 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:

74. Nonmagnetic impurities not detrimental to SC BaFe 1.8 Co 0.2 As 2 : Tc~22K Fe replaced by Co Impurities do not destroy SC (like Zn doping in cuprates) No signature of Curie-Weiss susc. F.L. Ning et.al, arXiv:0808.1420

75. 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): Bad insulator Bad metal 1B HB model (plaquette):

76. DMFT for a simple system Identify correspondence between the local and impurity quantities: Identify correspondence between the local and full GF: Solve QIM: Equivalent to summation of all local Feynman diagrams A. Georges & G. Kotliar, RMP 1996

77. Iron SC: How it all started …. Published in Chemical journal (Journal of American Chemical Society) Received January 2008, published online Feb 2008

78. And exploded…. more than 23 cond-mat’s in March 2008 >260 preprints at the end of July mostly from China!

79.  R=(0,0)  R=(1,0)  R=(1,1) Reference systems Reference system in DFT: Kohn-Sham system of independent electrons Reference system in DMFT: One interacting atom + system of independent electrons Interacting cluster+ system of independent electrons Kohn-Sham: Potential is local and static Self-energy is short ranged and retarded Obtained by solving a QIM