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Superconductivity in CaC 6 , a heavily electron-doped graphite

Superconductivity in CaC 6 , a heavily electron-doped graphite. L.Boeri , J.S.Kim, R.Kremer, O.K.Andersen, MPI-FKF, Stuttgart, Germany Feridoon. S. Razavi, Brock Univ, Canada G.B. Bachelet, Università la Sapienza, Roma, Italy M. Giantomassi, UCL, Louvaine-la-Neuve, Belgium.

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Superconductivity in CaC 6 , a heavily electron-doped graphite

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  1. Superconductivity in CaC6, a heavily electron-doped graphite L.Boeri, J.S.Kim, R.Kremer, O.K.Andersen, MPI-FKF, Stuttgart, Germany Feridoon. S. Razavi, Brock Univ, Canada G.B. Bachelet, Università la Sapienza, Roma, Italy M. Giantomassi, UCL, Louvaine-la-Neuve, Belgium Workshop on Electronic Structure of Emerging Materials Theory & Experiment February 2007, Lonavla, India.

  2. T.E. Weller, M. Ellerby, S.S. Saxena, R.P.Smith, N.T. Skipper, Nature Physics 1, 39 (2005). “Superconductivity in the Intercalated Graphite compounds C6Yb and C6Ca” Tc=11.5 K (CaC6) and 6.5 K (YbC6) … WHY is it so interesting ? • Highest Tcamong the Graphite Intercalation Compounds. ? Can e-ph theory explain Superconductivity in CaC6 or is there an exotic pairing mechanism ? (acoustic plasmons). What can we learn ? • 2001: Tc 40 K was foundin MgB2, a heavily hole-doped graphite. ? What happens when we dope with electrons? (CaC6 and other GICs)

  3. A few facts about Electron-Phonon Superconductors: ωlog:Prefactor:Light elements have high vibrational frequencies λ:Exponent:the larger the coupling, the higher Tc μ*:Exponent:Coulomb repulsion hinders Tc Highest Tc: MgB2, Tc=39 K! (2001) LDA and superconductivity: ! Calculate phonon frequencies and e-ph coupling constant from first-principles using DFPT! ? Which phonon and electronic states are responsible for the coupling ?

  4. Electrons (CaC6) Interlayer π* π Interlayer NMTO Wannier function Holes (MgB2) σ <int/H/π*>=0 π π* - + + + The interlayer band cannot interact with the π* band, but only with the bonding π (the interlayer and π* bands always cross) + - + + + + - + + + + -

  5. In all superconducting Graphite Intercalation Compounds the interlayer band is occupied! PRESSURE CHARGE G.Csànyi, P.B. Littlewood, A.H. Nevidomskyy, C.J. Pickard, B.D. Simons, Nature Phys.1,42(2005).

  6. CaC6 C6(prim. graph.) Doping with Electrons, CaC6: • Electronic Structure: • Intercalating a Ca atom between the C planes moves the IL band down in energy. • In CaC6 there are two types of bands at the Fermi level: Interlayer and π*. • All the superconducting GICs have • Interlayer and π* bands at EF. • NMTO orbitals: • The IL orbital has an axial symmetry and is localized between the planes. • In CaC6 the orbital has a partial 3z2-1 character.

  7. Metal Dielectric Metal Which is the superconducting mechanism ? Acoustic plasmons ? (G. Csànyi et al., Nature Physics 2005). Basic assumptions: 2D metallic electrons (interlayer ?) sandwidched between dielectric layers. A. Bill et al, PRB (2003) NO! IL electrons are 3D in character! ! Electron-phonon interaction I. Mazin, PRL (2005), M. Calandra and F. Mauri PRL (2005) and J.S. Kim et al., PRL (2006) and PRB (2006), L.Boeri et al., cond-mat/0701347.

  8. CaC6: Phonon Dispersions and e-ph coupling Cxy Cz Ca M. Calandra and F. Mauri PRL (2005) and J.S. Kim et al., PRB (2006).

  9. CaC6: Specific heat CaC6 samples and experiments from J.S. Kim and R. Kremer (MPI Stuttgart) Normal State: Electronic term: Lattice term: Large T5 term at low T <-soft Einstein mode (Ca)! Superconducting State: s-wave superconducting gap : No gap node!! (consistent with pen. depth) J. S. Kim, R.K. Kremer, L.B., F. Razavi, PRL (2006)

  10. Effect of Pressure: Experiment: Tc increases with Pressure. Can LDA explain why? • Structural optimization: • We calculate the structure for different P • Compressibility is anisotropic kc/ka~9. • Hydrostatic pressure reduces c/a considerably. • Electronic structure: • The interlayer band is pushed up in energy -> increasing charge transfer to the π* bands. • N(0) decreases! To increase Tc we need a soft phonon mode!

  11. DFT: Increase of Tc with P(0 ->100 kbar) This is close to the upper limit for Tc because of lattice instability (12 GPa) *! J.S. Kim, L.Boeri, F.S. Razavi, R.K. Kremer, cond-mat/0603530. * Confirmed by experiments (Gauzzi et al, cond-mat/0603443).

  12. What is the e-ph interaction of pure graphite? 2/3 e—doped graphite: fill the interlayer band without intercalant: Charge between the plane shifts int. band ~2 eV down in energy. 2 types of bands at the EF: Interlayer + π* (Jellium Intercalated Graphite, JIG). 2 peaks inα2F(ω)!!! Cxy 80% of λ from C(z) modes Cz In this case we exploit the strong dormant e-ph interaction between π and Interlayer bands! L. Boeri, G.B. Bachelet, M. Giantomassi, O.K. Andersen, cond-mat/0701347.

  13. INTERLAYER-π* coupling Effect of an out-of-plane buckling phonon on the band structure of 2/3 e- doped graphite. Strong Interband coupling between π and IL electrons!

  14. Conclusions and Open Issues: • 2005: Discovery of superconductivity in CaC6 and YbC6 (heavily hole-doped) • Csànyi et al.: superconductivity appears when the interlayer band is full. Pairing mechanism: acoustic plasmons or e-ph coupling ? • LDA: intermediate coupling to Caxy and Cz phonons + Specific heat: BCS-like, isotropic s gap + Pressure dependence of Tc: -> e-ph theory is plausible! Can we say anything general about e-ph interaction in doped graphite ? Dormant e-ph interactions Hole-doped:MgB2(2001) Electron-doped: CaC6, YbC6(2005) σ bands + bond-stretching phonons Interlayer & π* bands + buckling phonons ? What about multi-walled nanotubes ?

  15. References: • L. Boeri, G.B. Bachelet, M. Giantomassi, O.K. Andersen, • “Electron-phonon interaction in Graphite Intercalation Compounds”, • cond-mat/0701347 • I. I. Mazin, L. Boeri, O.V. Dolgov, A.A. Golubov, G.B. Bachelet, M. Giantomassi, O.K.Andersen, • “Unresolved problems in superconductivity of CaC6”, Physica C, in press. • J. S. Kim, L. Boeri, R. K. Kremer, F.S. Razavi, • “ Effect of Pressure on Superconducting Ca-intercalated Graphite CaC6”, Phys. Rev. B 74, 214513 (2006). • J. S. Kim, R. K. Kremer, L. Boeri,F.S. Razavi, • “Specific Heat of the Ca-Intercalated Graphite Superconductor CaC6” • Phys. Rev. Lett. 96, 217002 (2006) . • M. Giantomassi, L. Boeri, and G. B. Bachelet, • “Electrons and phonons in the ternary alloy CaAl2−xSix as a function of composition”, Phys. Rev. B 72, 224512 (2005) .

  16. IL electrons and e-ph coupling are strongly sensitive to interlayer distances…

  17. This is also observed in real GICs… Cxy Ixy Cz c increases Tc decreases! M. Calandra and F. Mauri, PRB (2006).

  18. Is this feature found in other layered superconductors? • YES! For example in CaAlSi • Same crystal structure as MgB2 Al and Si sit on a hexagonal layer • Tc=7.7 K • Al and Si concentration can be varied in a wide range • E-ph coupling, stability and • Superconductivity are governed by buckling phonons and π*+ interlayer bands

  19. CaAl2in the optimizedAlB2structure is very differentfrom MgB2! Few σ holes! Dynamically unstable! M. Giantomassi, L.Boeri, G.B. Bachelet, PRB 72, 224512 (2005).

  20. Increase of Tc with P:Theory vs. Experiment (Exp. Data from Gauzzi et al, cond-mat/0603443). • Experiments and theory show that the increase in Tc is limited by lattice instabilities… • Theory predicts a slower increase in Tc than shown by the experiment

  21. DFT: Effect of pressure on the phonon spectrum • All phonon modes harden with pressure, except for the low-lying Ca in-plane modes, which soften. • At P~120 kbar these modes • drive the system unstable (rearrangement of the Ca sublattice ) • A similar instability has been observed experimentally at 8 Gpa in CaC6 by Gauzzi et al. (cond-mat/0603443)

  22. Open Issues (1): Structural transition A. Gauzzi et al., cond-mat/0603443

  23. Open Issues (2): Linear Hc2

  24. Open Issues (3): Isotope effect Ca Isotope isotope effect coefficient, α = 0.50(7). D.G. Hinks, et al. condmat/0604642

  25. Electronic structures of CaC6 under pressure N (EF) decreased under pressure ! Already questionable at ambient pressure, but… c-axis dispersion enhanced under pressure More 3D under pressure ! Pairing contribution from acoustic plasmon decreased!! J.S. Kim et al., cond-mat/0603530.

  26. First-Principles Calculations: The most relevant properties of electron-phonon superconductors can be calculated from first-principles using Density Functional Perturbation Theory (Linear Response), Phonon Spectra E-ph Matrix Elements Eliashberg Spectral Function This function describes the spectral distribution of the e-ph coupling over different phonon branches...

  27. Doping with holes: MgB2is to date the e-ph superconductor with the highest-Tc! • The total e-ph coupling λ=0.8-0.9 is concentrated in a doubly-deg. bond-stretching mode <-graphite! Y. Kong et al., PRB 64, 02051 (2001) D Strong geometrical coupling betweenbond-stretching modes andstiffbonds!

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