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Spin-fluctuation–mediated pairing in multiband superconductors

Spin-fluctuation–mediated pairing in multiband superconductors. Maxim M. Korshunov. Divergence of the electron-electron scattering vertex. For , :. =. Determines Copper instability. Hubbard model. U. t k. RPA Spin susceptibility.

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Spin-fluctuation–mediated pairing in multiband superconductors

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  1. Spin-fluctuation–mediated pairing in multiband superconductors Maxim M. Korshunov [ФМЯ-Октябрь-2012]

  2. Divergence of the electron-electron scattering vertex For , : = Determines Copper instability

  3. Hubbard model U tk RPA Spin susceptibility N.F. Berk and J.R. Schrieffer, PRL 17, 433 (1966)

  4. c0 Vs c0 c0 Spin-fluctuation mediated interaction Effective interaction from spin fluctuations (Berk and Schrieffer 1966, Scalapino et al. 1989-1996) Magnetic instability:

  5. Numerical results (FLEX) D. Manske, Theory of Unconventional Superconductors, Springer-Verlag (2004) S. Graser, T.A. Maier, P.J. Hirschfeld, and D.J. Scalapino, NJP 11, 025016 (2009)

  6. Effective dimensionless coupling From the stationary condition one can find the eigenvalue problem: D.J. Scalapino, E. Loh Jr., and J.E. Hirsch, PRB 34, 8190 (1986)

  7. Matrix elements: orbitals → bands 5-orbital tight-binding model Matrix elements: Interactions in band space become effectively momentum-dependent! S. Graser, T.A. Maier, P.J. Hirschfeld, and D.J. Scalapino, NJP 11, 025016 (2009)

  8. Multiorbitaldynamical spin susceptibility

  9. Diagrams for

  10. RPA for is a matrix with indices where “–” is due to the bubble

  11. RPA for We assume that

  12. RPA for where “–” is due to the bubble

  13. RPA for Similarly,

  14. RPA for If Check: single-band case That is exactly the single-band RPA solution for

  15. Interactions in the RPA

  16. Few easy steps to get pairing 1. Calculate pairing interaction in the orbital basis 2. Transform to the band basis 3. Solve eigenvalue problem and find the gap function and the corresponding eigenvalue S. Graser, T.A. Maier, P.J. Hirschfeld, and D.J. Scalapino, NJP 11, 025016 (2009) A.F. Kemper et al., NJP12, 073030 (2010)

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