Hague, J. P.
Superconducting states of the quasi-2D Holstein model: effects of vertex and non-local corrections.
Journal of Physics: Condensed Matter, 17(37) pp. 5663–5676.
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I investigate superconducting states in a quasi-2D Holstein model using the dynamical cluster approximation. 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 Bardeen–Cooper–Schrieffer approximation.
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