1. Superconductivity in electron-doped C 60 crystals 電子ドープされたフラーレン結晶 における超伝導 Kusakabe Lab Kei Kawashima

2. Contents Introduction – History of superconductivity Electron-doped C 60 crystals – Interesting points – Crystal structures – Electronic structures with first-principles method Future works Summary

3. History of superconductivity The first superconductor Hg (Tc=4K) The first superconductor Hg (Tc=4K) The first molecular crystal supeconductor High-Tc copper oxides High-Tc copper oxides Electron-doped C 60 supeconductors Ref: KURENAI : Kyoto University Research Information Repository

4. Electron-doped C 60 crystals - Interesting points - A C 60 molecule itself has interesting structure. A C 60 crystal is semiconductor, and it has wide varieties of application. In addition, it transfers to a superconductor when some electrons are doped. There are many interesting themes to study. – The types, and the number of atoms doped – Pressure dependences of electronic structure and Tc – Many C 60- based crystals are BCS-type superconductor

5. Electron-doped C 60 crystals - crystal structures -

6. Electron-doped C 60 superconductors Cs 3 C 60 (A15) Valence (The number of doped-electrons per C 60 molecule) BCS (Electron pair by phonon-electron interaction) Non-BCS (Electron pair by electron-electron interaction etc.) 3 K 3 C 60,RbK 2 C 60, Rb 2 KC 60 Rb 3 C 60, Rb 2 CsC 60,RbCs 2 C 60 (All FCC) Cs 3 C 60 (A15) (Maximum Tc=38K under 7kbar) 8 Ba4C60(BCO) 9 A 3 Ba 3 C 60 (BCC) (A=Alkali earth) 10 A 2 Ba 4 C 60 (BCC), Ca 5 C 60 12 Sr 6 C 60 (BCC), Ba 6 C 60 (BCC) K 3 C 60 (FCC)

7. Tc of BCS-type superconductors Material Lattice constant Calculated Tc Experimental Tc Calculation method K 3 C 60 14.253 Å 16.7K 19.28K First-prinsiple self-consistent density functional theory (DFT) in local density approximation (LDA). Wave functions are expanded by OLCAO method. RbK 2 C 60 14.299 Å 21.7K 21.80K Rb 2 KC 60 14.364 Å 24.6K 25.40K Rb 3 C 60 14.436 Å 28.6K 29.40K Rb 2 CsC 60 14.493 Å 34.3K 31.30K Ref : Ming-Zhu Huang et al. Physical Review B, Volume 46, Number 10, 6572-6577 (1992)

8. Method for study - First principles calculation -

9. Band structures C60(FCC)-Insurator K3C60(FCC)-Metal Ba6C60(BCC)-Semimetal Unoccupied Occupied Fermi energy Ref: ・ O. Gunnarsson, Reviews of Modern Physics, Vol. 68, No. 3, 575-606(1996) ・ Steven C. Erwin, Phys. Rev. B, Vol. 47 No.21, 14657- 14660(1993) t 1u t 1g huhu

10. Pressure depencences Cs 3 C 60 (Non-BCS-type) K 3 C 60 (BCS-type) Ref: Ming-Zhu haung et al. Phys, Rev. B, Vol. 47, NO. 13(1992) Ref: ALEXEY Y. GANIN et al. Nature Mat., Vol. 7(2008) Ambient Pressure Pressure =0.33GPa Pressure =4.65GPa

11. Future works I calculate the electronic structures of C 60 and electron-doped C 60 crystals, such as band structure, fermi-surface, and DOS, with first principles method. After the calculations, I compare the results with those of other groups and experimental results, to analyze the electronic structures of crystals calculated.

12. Summary A C 60 crystal itself isn’t superconductor. It transfers to a superconductor when electrons are doped. Electron-doped C 60 s have different electronic structure and T c because of the differences of the type and the number of atoms doped. Electronic structure and T c also change with applied pressure.

13. Picene superconductor Picene molecule C 22 H 14 Picene crystal Monoclinic lattice 2 molecules in a basis E g ≒ 3.3ev

14. T c vs doping density of alkali-metal

15. Electronic structure with First-principles method Fermi surface Density of states Band structure

16. What is superconductivity? Perfect diamagnetism Perfect conductivity Meissner effect 2 main Characters of superconductivity Paramagnetism(Metal) Perfect diamagnetism(Superconductor) Magnetic field

17. History of superconductivity Year191119862006 Discovery The first superconductor Hg was discovered High-T c CuO 2 system superconductor was discovered Fe-based system Superconductor was discovered Highest-T c A few KAbout 163 KAbout 55 K Pypical superconduct ors in those days Hg, Pb, Nb, NbC, NbN, NbGe, MgB 2 (Tc ≒ 40K) YBaCuO, LaBaCuO, BiSrCaCuO, TiBaCaCuO, HgBaCaCuO LaAsFeO, LiFeAs, BaFe 2 As 2, SmFeAs FeSe,FeTe,FeS LaPFeO

18. Applications of superconductivity Linear motor car : Superconductive magnet MRI: Superconductive magnet, SQUID Superconductive computer

19. An example of band structure and fermi-surface with ARPES Band structure Fermi surface