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Calculation of superconducting critical temperature of hole-doped CuAlO 2 and CuAlS 2

Calculation of superconducting critical temperature of hole-doped CuAlO 2 and CuAlS 2. Yoshida lab Hiroki Uede. 10/02 M1 colloquium. Index. Introduction - Electron-phonon superconductivity - - Allen-Dynes formula - P revious work - Delafossite structure CuAlO 2 - M y work

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Calculation of superconducting critical temperature of hole-doped CuAlO 2 and CuAlS 2

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  1. Calculation of superconducting critical temperature of hole-doped CuAlO2 and CuAlS2 Yoshida lab Hiroki Uede 10/02 M1 colloquium

  2. Index • Introduction - Electron-phonon superconductivity - - Allen-Dynes formula - • Previous work - Delafossite structure CuAlO2 - • My work - Chalcopyrite structure CuAlS2 - • Summary • Future plan

  3. Introduction

  4. Electron-phonon interaction If attractive interaction between electrons exist, electrons near the Fermi surface form Cooper pair, and fall into lower energy. The attraction is attributed to an “electron-phonon interaction” + Cooper pair

  5. The Allen-Dynes formula λ : electron-phonon interaction ωlog : the logarithmic averaged phonon frequency μ* : screened Coulomb interaction assumed α2F(ω) : Eliashberg function N(εF) : electronic density of states at the Fermi level εF ωνq and εk : phonon and electron energies : the electron-phonon matrix elements P. B. Allen and R. C. Dynes: Phys. Rev. B 12 (1975) 905.

  6. Previous work Akitaka Nakanishi , Hiroshi Katayama-Yoshida:Solid State Commun. 152 (2012) 24–27

  7. Crystal structure of CuAlO2 • Delafossite structure hexagonal • p-type transparent semiconductor Cu Al O

  8. Rigid band model doped-system non-doped system the number of valence electrons reduce Fermi energy εF number of electrons at Fermi energy N(εF) band structure phonon dispersion not change eigenvalue εk phonon frequency electron-phonon matrix electron-phonon interaction λ the logarithmic averaged phonon frequency ωlog superconducting critical temperature TC assumed

  9. Results1 Density of State(DOS) Band dispersion CuAlO2 has flat band near Fermi level, and this band is Cu- and the O-2pz anti-bonding π-band

  10. Results2 Tc and λvs. Nh TC Electron–phonon interaction λ and logarithmic averaged phonon frequencies ωlog. Tc has max and minatNh = 0.3, 1.0. Nh λ increase →　TC increase at Nh=0.3

  11. O O O O Results3 phonon dispersion Nh＝0.3() Nh＝1.0() phonon mode that stretches the O–Cu–O dumbbell has a strong interaction with electrons of the flat band in Cu-and the O-2pz anti-bonding π-band Phonon dispersions and electron-phonon interactions of hole-doped CuAlO2. The radius of circle represents the strength of partial electron-phonon interaction . Note that many are very small and their circles are no longer invisible. (a) The number of holes Nh = 1.0. (b) Nh = 0.3. Cu Cu

  12. My work

  13. Motivation CuAlO2 (Delafossite structure) CuAlS2TC= ? [K] (chalcopyrite structure) valence electron O:2p 　　　　↓ S:3p

  14. Purpose • Calculate electron-phonon interaction λ and superconducting critical temperatureTCof CuAlS2 based on rigid band model and Allen-Dynes formula • Compare delafossite structure (two dimensional) CuAlO2 with chalcopyrite structure (three dimensional) CuAlS2

  15. Crystal structure of CuAlS2 • Chalcopyrite structure • tetrahedral coordination • semiconductor Cu Al S

  16. Computational method-electric structure & phonon dispersion- • Quantum-Espresso code • Based on Density Functional Theory (DFT) • Generalized Gradient Approximation (GGA) • Ultra-soft pseudo potential • 8×8×8 k-point grid (electron) 8×8×8 q-point grid (phonon) • Cut-off energy for wave function is 40 [Ry] • Cut-off energy for charge density is 320 [Ry]

  17. Band dispersion Energy = 0 is Valence Band Maximum (VBM) Eg=1.65 [eV] Γ Γ *U.P. Verma , Per Jensen , Monika Sharma , Poonam Singh: Computational and Theoretical Chemistry 975 (2011) 122–127 **J.E. Jaffe, A. Zunger, Phys. Rev. B 28 (1983) 5822

  18. Density of states (DOS) Energy zero is the top of the valence band Maximum (VBM).

  19. Density of states (DOS) anti-bonding state (Cu 3dεand S 3p) bonding state (Cu 3dεand S3p) non bonding state (Cu3dγ) Energy zero is the top of the valence band Maximum (VBM).

  20. Phonon dispersion Γ Γ

  21. Phonon dispersion CuAlO2 (Delafossite structure) CuAlS2 (Chalcopyrite structure) Γ Γ S atom is heavier than O atom →　Max phonon frequency of CuAlS2 lower than that of CuAlO2

  22. Summary • I introduce Allen-Dynes formula. • I introduce previous work. CuAlO2 has based on rigid band model. • I show results of band dispersion ,DOS ,and phonon dispersion of CuAlS2

  23. Future plan • I will calculate TC vs. number of holes about CuAlS2 • I will consider difference of dimensionality and Tc • I will calculate other chalcopyrite structures. CuAlS2 CuGaS2 AgAlS2 AuAlS2 CuInS2

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