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

TL;DR

This paper demonstrates that vertex corrections in Eliashberg theory can induce a stable odd-frequency spin-triplet superconducting state that coexists with the conventional even-frequency state, confirmed through self-consistent calculations.

Contribution

It reveals a new mechanism for odd-frequency superconductivity induced by vertex corrections, showing coexistence with even-frequency superconductivity in a cuprate model.

Findings

Both superconducting gaps are finite over a wide temperature range.

The odd-frequency gap is an order of magnitude smaller than the even-frequency gap.

The study provides a proof of concept for the coexistence of both states in bulk materials.

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.