Physics – Condensed Matter – Superconductivity
Scientific paper
2007-04-02
J. Phys.: Condens. Matter vol. 17 (2005) 5663-5676
Physics
Condensed Matter
Superconductivity
Reprint to improve access. 14 pages. 10 figures.
Scientific paper
I investigate superconducting states in a quasi-2D Holstein model using the dynamical cluster approximation (DCA). The effects of spatial fluctuations (non-local corrections) are examined and approximations neglecting and incorporating lowest-order vertex corrections are computed. The approximation is expected to be valid for electron-phonon couplings of less than the bandwidth. The phase diagram and superconducting order parameter are calculated. Effects which can only be attributed to theories beyond Migdal--Eliashberg theory are present. In particular, the order parameter shows momentum dependence on the Fermi-surface with a modulated form and s-wave order is suppressed at half-filling. The results are discussed in relation to Hohenberg's theorem and the BCS approximation.
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