1. (conventional) phonon SC 2. Unconventional cuprates SC 3. Fe-based SC

1. Quest for Higher Tc or RTS 3 possible routes: 1. (conventional) phonon SC 2. Unconventional cuprates SC 3. Fe-based SC Under extreme conditions: 1. H3S under Extremely high pressures 2. YBCO under pulsed Laser pumping 3. Monolayer FeSe on an STO substrate

2. Sulfur Hydride @200 GPa : Phonon-SC (?) A.P. Drozdov, M.I. Eremets, I.A. Troyan, arXiv:1412.0460. A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontv & S.I. Shylin, Nature 525, 73 (2015). (Max Planck, Mainz) Tc = 203 K Im3m: H3S (?) Theoretical prediction: “P-induced metallization of dense (H2S)2H2 with high-Tc superconductivity” D. Duan et al., Sci. Reports 4, 06968 (2014). (Jilin Univ., Changchun)

3. S atoms form a bcc sublattice. D. Duan et al., Sci. Reports 4, 06968 (2014). arXiv: 1509.03156 Structural analysis cannot distinguish between R3m and Im-3m.

4. Rules of Matthias for Discovering New Superconductors #1: Findcubic crystals, high symmetry is best. #2: Find d-electron metals and/or metals with the average number of valence electrons, preferably odd numbers 3, 5, and 7,peaks in DOSare good. #3: Stay away frommagnetism, exclude metals showing or in close vicinity of magnetism. #4: Stay away fromoxygen and insulators, exclude metals near a metal-insulator transition such as oxide materials. #5: Stay away from theorists

5. A15 Superconductors Tc (K) Liq. N２ Liq. H２ 1973 Tc = 23 K Liq. He year

6. Strong electron-phonon interaction in A15 Strong phonon scattering at elevated T’s  Very short mean free path, l~a(orkFl≤2p) Resistivity saturation Cu

7. BCS Tc Limit/Tc Ceiling ? Tc (K) Liq. N２ BCS limit ? Liq. H２ 1973 Tc= 23 K Liq. He year

8. 200 History of Phonon High-Tc Tc(K) 100 ~ 30 K MgB2 39 K C60 BaKBiO3 Nb3Ge 23 K 2014 2001 1988, 1991 1973 0 1970 1980 1990 2000 2010 year

9. Tc bound (ceiling) of “phonon” SC (BCS-Migdal) kBTc ~ ħW0e-1/l (l= N(EF) <I 2> / MW02) kBTc≪ħW0≪EF For very largeW0and moderatel, no Tcceiling as long asħW0≪EF “Metallic Hydrogen: A High-Temperature Superconductor?” N.W. Ashcroft, Phys. Rev. Lett. 21, 1748 (1968).

10. Tc bound (ceiling) of “phonon” SC Migdal-Eliashberg (McMillan-Allen-Dynes) ħ<w> kBTc Weak to moderate el-ph coupling: kBTc ~ ħW0e-1/l For very largeW0and moderatel, no Tcceiling as long asħW0≪EF Migdal Strong el-ph coupling: For largel; Tc ~l1/2 No Tc ceiling as long as a lattice instability can be avoided.

11. Doped Bismuthate (BaBiO3) O Strong electron-phonon coupling Strong electron-phonon coupling Bi Ba Superconductivity (Tc max~ 12, 30 K) is unstable against CDW formation. L.F. Mattheiss et al., Phys. Rev. B 37, 3745 (1988). A.W. Sleight et al., Solid State Commun. 17, 27 (1975). R.J. Cava et al., Nature 332, 814 (1988).

12. Parent Insulator BaBiO3 3D-CDW Bi5+ Bi3+ Superconductor CDW Insulator Breathing-mode distortions T.M. Rice & L. Sneddon, Phys. Rev. Lett. 47, 689 (1981). S. Tajima, SU et al., Phys. Rev. B 32, 6302 (1985). CDW gap S. Uchida, K. Kitazawa, S. Tanaka, Phase Transitions 8: 95-128 (1987).

13. IR & Raman phonons in BaBiO3 IR-active Raman-active BaBiO3 \\ breathing mode BaBiO3

14. Resonant Raman scattering from the breathing-mode phonon in BaBiO3 breathing mode CDW gap 2-phonon tuning incident light energy l = 5145 Å 3-phonon 4-phonon

15. Strong covalent bond and strong electron-phonon coupling in BaBiO3 Extremely large deformation potential for breathing-mode lattice distortions s-bonding Bi6s-O2pbandsspread over ~ 16 eV breathing mode L.F. Mattheiss & D.R. Hamann, Phys. Rev. B 28, 4227 (1983).

16. Relativistic Effect on Atomic Energy Levels P3/2 P3/2 S1/2 s, p P1/2 P1/2 j = l + s S1/2 “non-relativistic” “spin-orbitinteraction” “mass-correction” Hso = (Z/137)2l·s m = m0/(1 – v2/c2)1/2

17. Charge Disproportionation (Valence Skipper) “ionic picture” (too simplified) 2Bi4+(6s)1 Bi3+(6s)2 + Bi5+(6s)0 Ba2+Bi4+O2-3 6p 6p 6p relativistic effect:“mass-correction” “closed shell” ~ (Z/137)2 Ry 6s 6s 6s Bi: Z = 83 “closed shell” 5s, 5p, 5d, …

18. Strong Covalent Bond in BaBiO3 BaBiO3 Antibonding BaBi1-xPbxO3 Doping CDW Gap Ba1-xKxBiO3 O2ps Bi6s：Bi4+ Bonding Bi4+(6s)1 Bi3+(6s)2 + Bi5+(6s)0

19. Strong Covalent Bond in MgB2 sp2-Antibonding (s *) B2px, 2py B2px, 2py Nonbonding Mg B2s B2s Charge Transfer s -band sp2-Bonding (s)

20. Superconductivity next to CDW SC often emerges from CDW phase, but Tc is not high compared to SC competing with AF (SDW) phase:i) phonon vs electronic pairing ? Ii) conventional s-wave vs unconventional pairs ?Iii) charge (e)vs spin (sx, sy, sz); 1:3 (Aoki)? E. Morosan, H.W. Zandbergen, N.P. Ong, R.J. Cava et al., Nature Phys. 2, 544 (2006). K.E. Wagner, R.J. Cava et al., Phys. Rev. B 78, 104520 (2008).

21. Superconductivity next to CDW Hole-doped cuprate two-leg ladders Sr14-xCaxCu24O41 @ P Tc max~ 12 K CuxTiSe2 12 8 Tc(K) No spin order 4 2 4 6 8 0 P (GPa) 3cL K.M. Kojima, N. Motoyama, H. Eisaki, SU, J. Electron Spectroscopy and Related Phenomena 117-118, 237 (2001). x ~ 11 (n=1/3) N. Motoyama, SU et al., Europhys. Lett. 58, 758 (2002).

22. Charge and SC orders are intertwined. Tc max~ 100 K 400 300 PG T* TemperatureT (K) 200 TSCon TCDWon 100 Tc FL AF d-SC 0 0.3 0 0.1 0.2 Hole dopingp QCP ?

23. Optimized Phonon Mechanism in MgB2 Mg B 1) Strong sp2bonding: Layer structure 2) Light element: Combined with the strongsp2bond makesW0very high. 3) A simple metal: ħW0≪EF(Migdal) 4)Strong electron-phonon coupling without instability: Cylindrical FS (s-FS) avoids a structural instability. These seem to conspire to optimize the phonon-mediated superconductivity in MgB2. W. E. Pickett, Physica C 468, 126 (2007).

24. “Covalent Bond Driven Metallic” Tc ~ 40 K ħW0 ~ 80 meV l ~ 1 MgB2: Mg2+(B2)2- s-band Bsp2hybridization s-bondingband J.M. An and W. E. Pickett, Phys. Rev. Lett. 86 (2001). s-FS

25. Doped Fullerides (C60)-Cs3C60 Basically isotropic s-wave pairing, but the highest Tc is realized in the vicinity of AF phase. A15-Cs3C60 P =7 kbar P A.Y. Ganin et al., Nature Mater. 7, 367 (2008).

26. 200 History of Phonon High-Tc 203 K H3S@200 GPa Tc(K) 100 30 K MgB2 39 K BaKBiO3 Nb3Ge 23 K 2014-15 2001 1988 1973 0 1970 1980 1990 2000 2010 year

27. Tc = 203 K Superconductivity in Sulfur Hydride (H3S) @ P=200 GPa Resistance Magnetization/ Meissner A.P. Drozdov, M.I. Eremets, I.A. Troyan, V. Ksenofontv & S.I. Shylin, Nature 525, 73 (2015).

28. Further Optimization Phonon Mechanism in H3S ? 1) Strong covalent bonding (H1s-S3p) 2) Light element: Combined with the strongbond makesW0very high. 3) A simple metal: ħW0≪EF(Migdal)?? 4) Strong electron-phonon coupling without instability: Non-nestingFS (s-FS) avoids a structural instability. Isotropic HTS suitable for SC power application N. Bernstein, I.I. Mazin et al., Phys. Rev. B 91, 060511 (2015).

29. Why does theory successfully predict high Tc in H3S? W. Sano, T. Koretsune, T. Tadano, R. Akashi, R. Arita, arXiv: 1512.07365. ● Quantum nature of H atom - zero-point motion -anharmonic vibrations ● Validity of Migdal theorem - van Hove singularity near EF The effective Fermi energy is small; ‘EF’ ~ ħW0 m* = m / [1 + m ln (EF/ħW0)] Y. Quan, W.E. Pickett, arXiv: 1508.04491. L.P. Gor’kov, V.Z. Kresin, arXiv: 1511.06926.

30. Quantum Hydrogen Bond in R3m I. Errea et al., Nature 532, 81 (2016). d1: Covalent bond d2: Hydrogen bond

31. Revival of Matthias’ Rules (?) #1: Findcubic crystals, high symmetry is best. #2: Findd-electron metals and/or metals with the average number of valence electrons, preferably odd numbers 3, 5, and 7, peaks in DOSare good. #3: Stay away frommagnetism, exclude metals showing or in close vicinity of magnetism. #4: Stay away fromoxygen and insulators, exclude metals near a metal-insulator transition such as oxide materials. #5: Stay away from theorists

32. Why does theory successfully predict high Tc in H3S? arXiv: 1512.07365

33. No Tc bound for “phonon” SC (?) McMillan-Allen-Dynes (assumingm*= 0.10-0.15) A. Bianconi: “SC above the lowest Earth temperature: 184 K (-89.2℃)” 3. H3S @ 200 GPa, Tc ~ 200 K kBTc =ħW0e-1/l W0 =(K/ M)1/2 ~ 200 meV, <w> ~ 1300 K, l ~ 2.2 2. MgB2 @ 0 Pa, Tc ~ 40 K kBTc =ħW0e-1/l W0 =(K/ M)1/2 ~ 80 meV, <w> ~ 600 K, l ~ 1 1. doped BaBiO3 , Tc ~ 30 K Unstable against CDW

34. No Tc bound for “phonon” SC (?) McMillan-Allen-Dynes (assumingm*= 0.10-0.15) 4. H @ 2000 GPa, Tc ~ 750 K kBTc =ħW0e-1/l W0 =(K/ M)1/2 ~ 400 meV, <w> ~ 2300 K, l ~ 3 J.M. McMahon & D.M. Ceperley, Phys. Rev. B 84, 144515 (2011). 3. H3S @ 200 GPa, Tc ~ 200 K kBTc =ħW0e-1/l W0 =(K/ M)1/2 ~ 200 meV, <w> ~ 1300 K, l ~ 2.2 2. MgB2 @ 0 Pa, Tc ~ 40 K kBTc =ħW0e-1/l W0 =(K/ M)1/2 ~ 80 meV, <w> ~ 600 K, l ~ 1 1. doped BaBiO3 , Tc ~ 30 K Unstable against CDW

35. Even Higher Tc in Atomic Metallic H @2TPa Phys. Rev. B 84, 144515 (2011). “Metallic Hydrogen: A High-Temperature Superconductor?” N.W. Ashcroft, Phys. Rev. Lett. 21, 1748 (1968). Tcmax ~ 750 K !! @ 2000 GPa ħW0 ~ 400 - 500 meV <w> = 2300 K l ~ 3

36. Supplementary Informations

37. Valence Skippers La

38. Charge Disproportionation (Valence Skipper) 2Tl2+(6s)1 Tl1+(6s)2 + Tl3+(6s)0 2Pb3+(6s)1 Pb2+(6s)2 + Pb4+(6s)0 6p 6p 6p relativistic effect:“mass-correction” “closed shell” ~ (Z/137)2 Ry 6s 6s 6s “closed shell” 5s, 5p, 5d, …

39. Relativistic Element Hg Why is Hg a ‘liquid’ metal at RT ? La

40. Relativistic effect in Hg: Weak bond due to “closed shell” electronic structure Hg1+(6s)1 Hg0 (6s)2 + Hg2+(6s)0 6p 6p 6p Hg relativistic effect:“mass-correction” “closed shell” ~ (Z/137)2 Ry 6s 6s 6s “closed shell” 5s, 5p, 5d, …