1. Materials Issues in Correlated Superconductivity G. Kotliar Rutgers University Work done in collaboration with Z. Yin, A. Kutepov, K. Haule, R. Nourafkan (Rutgers) Supported by the AF MURI Towards New and Better Superconductors. MURI TEAM: PI Mac Beasley TEAM MEMBERS Bob Cava,, Ian Fisher, Ted Geballe, Bob Hammond Emilia Morosan 1 MURI review workshop. Better and Higher Temperature Superconductors Santa Barbara 12-16 December 2001

2. OUTLINE-CONCLUSIONS Origin of correlations. Very high dimensional space of materials and the relevant directions. What are the different sectors or families of correlated materials ? What are the relevant variables ? Materials proximate to Mott or CT insulators. Kappa Organics. Copper Oxides. Hubbard U, Charge Transfer (p-d) Energy Hunds Metals. Transition Metal Pnictides and Chalchogenides. Correlations governed by Hunds rule J and crystal fields Proximate to valence instabilities, Ba{1-x}KxBiO3 Tc~30 K. Correlation enhanced orbital -electron phonon coupling. Bismuthates puzzles. Proposed resolution: correlation enhancement of the electron lattice coupling relative to DLA. “The other high temperature superconductors” [W. Pickett Physica B 396, (2001) 112] fit also the same paradigm : after correcting for the delocalization error of LDA, a stronger coupling is obtained. 2

3. Real Space Structure. Ba 2+ O3 6- Bi 4+ Atomic Bi external shell Bi 6s^2 6p^3 Bi 4+ 1 sp electron per site. Valence skipping. Bi4+ disproportionates to Bi3+ and Bi5+ Pb substitution. Empties band from electrons.”Bi 5+”

4. onsite energy: Bi 6s: -6.54 eV O 2p orbital along the Bi-O bond: -4.92 eV hopping parameters: Bi 6s to O 2p along the Bi-O bond: -2.08 eV next nearest neighbor hopping of O 2p to O 2p orbital along the Bi-O bond, -0.87 eV. Bandwidth ~ 4.5 ev

5. CD W]] SC What are the relevant variables ? B site ? Disorder ? Vbi =4+ Vbi=5+ Vbi=4+ 3

6. Bismuthates S-wave Superconductor 2  /Tc ~ 3.5 -4 So why talk about correlations ? LDA fails to produce the breathing distortion and a gap in BaBiO3. Superconductivity near a structural /breathing /valence / CDW / instability boundary. Conflicting estimates of l from the same spectroscopy (with different analysis )    Different issue: conflicting results of the same experiment, isotope effect .4 vs.2 4

7. Theoretical Ideas, conventional electron phonon mediation vs electronic negative U (Varma PRL 61 713 (1988) Meregalli and Savrasov PRB 57, 14453 (1998) =.34 not sufficient to give 35 K Tc. Examination of configurations in the solid state without lattice relaxation result in positive U Harrison PRB 74 245128 (2006) Vielsak and Weber PRB 54, (1966) constrained DFT results in positive U. Both statements run into difficulties when confronated with state of the art ab-initio calculations. 5

8. Theoretical Approach LDA GGA suffers from the “delocalization error”, tendency to spread out the electronic density artificially. Underestimates: the barriers, of chemical reactions, the band gaps of materials, the energies of dissociating molecular ions, charge transfer excitation energies. Overestimates: binding energies of charge transfer complexes, spontaneous and induced polarization LDA overestimates the screening,near insulating states, and as a result understimates electron phonon coupling, tendency to polaronic effects etc. Overscreening can be corrected with hybrid functionals, B3LYP, or HSE. LDA also suffers from not being able to represent multislater determinants situations, for example near breaking bonds. DMFT corrects for that. 6

9. Theoretical Approach Francini et. al PRL 102, 256402 (2009) PRB 81, 085213 (2010) HSE functional gives the correct optical (2 ev) and indirect (.65 ev) gaps in BaBiO3, (as well as correct breathing distortion). Polaronic states presist at finite doping. Yin Kutepov and GK arXiv:1110.5751. Reconsider the srength of the electron phonon coupling using HSE. Metallic BaKBiO3 has  ~ 1. Bi 3+ and Bi 5 + have are not very different in charge (10-15 % ) but quite different orbital content. Insulator is strongly correlated. Metal intermediate correlations. Consistent with the estimations from early tunnelling Q Huang et. al. Nature 347, (1990) 370. Explains many other “anomalous” materials. 7

10. D Deformation potential. BBO and BPO Breathing Tilting BBO: GGA: 7.6 eV/A HSE: 13.3 eV/A BPO: GGA: 10.1 eV/A HSE: 11.2 eV/A Key ideas: L. F Matthiss, E. M Gryorgy D. W Johnson PRB 37 (1988) 3745. But implemented with much more powerful electronic structure functionals!! ~D 2 HSE~1 8

11. Expts. Pushkov et al.DMFT calculations R. Nourafkan and GK The optical conductivity in the metallic region can be understood with ~.9.   9

12. Valence Sikppers: Ruddleser Popper series A n+1 B n O 3n+1 10

13. Deformation potential: Ba 3 Bi 2 O 7 Breathing Tilting GGA: ~0 eV/A HSE: ~0 eV/A 11

14. Lambda and Tc vs x Ba 1-x La x PbO3 12

15. Dope with electrons via intercalation Tc=25 Na.3 HfNCl Yamanka et. al. Transition Metal Nitrides MNX, M = Ti, Zr, Hf; X= Cl, Br …. Why does Tc appear when you dope with electrons ?? Why does Tc depend weakly on doping ? Why is Hf better than Zr ? 13

16. Deformation potential: HfNCl Hf N vibration along the z axis GGA: 4.4 eV/A HSE: 5.3 eV/A 14

17. Cs 2 Au 2 Cl 6 Cubic: Pm-3m (221) Tetragonal: I4/mmm (139) Au 2+ Au 1+ Au 3+ In-plane stretching c-axis stretching Distortion: Cl in-plane breathing, difference in Au-Cl bonding: 0.76 angstrom c-axis stretching, difference in Au-Cl bonding: 0.91 angstrom Pressure restores the equivalence of the Au sites. 16

18. Optical properties: Cs 2 Au 2 X 6, X=Cl, Br, I Expts N. Kojima, Bull. Chem. Soc. Jpn., 73, 1445 (2000). Theoretical calculations Z. Yin ( Rutgers ) 17

19. Deformation potential: CsAuCl 3 GGA: ~1.6-2.5 eV/A HSE: in progress Jahn-Teller 18

20. Summary The unifying theme of these “Other High temperature superconductors “is that after correcting for the additional polarization resulting from the localization of charge which is lacking in LDA, there seems to be enough coupling to lattice+ electronic polarization to give observed Tc. [ Z. Yin, A. Kutepov and G. Kotliar, submitted to PRL] Current work: scanning for Tc higher than 30 K. Many Tl based systems. 15