Induced odd-frequency superconducting state in vertex-corrected Eliashberg theory

Abstract

We show that vertex corrections to Migdal's theorem in general induce an odd-frequency spin-triplet superconducting order parameter, which coexists with its more commonly known even-frequency spin-singlet counterpart. Fully self-consistent vertex-corrected Eliashberg theory calculations for a two-dimensional cuprate model, isotropically coupled to an Einstein phonon, confirm that both superconducting gaps are finite over a wide range of temperatures. The subordinate d-wave odd-frequency superconducting gap is found to be one order of magnitude smaller than the primary even-frequency d-wave gap. Our study provides a direct proof of concept for a previously unknown generation mechanism of odd-frequency superconductivity as well as for the generic coexistence of both superconducting states in bulk materials.

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