Odd-frequency Berezinskii superconductivity in Dirac semimetals

TL;DR

This paper develops a theoretical framework for odd- and even-frequency superconductivity in Dirac semimetals, highlighting conditions favoring Berezinskii pairing and proposing experimental signatures such as cusp-like features in the density of states.

Contribution

It introduces a general model for odd-frequency pairing in Dirac semimetals, showing how interactions influence pairing types and identifying experimental signatures.

Findings

Repulsive interactions favor Berezinskii pairing.

Attractive interactions support BCS pairing.

Density of states exhibits cusp-like features as signatures.

Abstract

We formulate a general framework for addressing both odd- and even-frequency superconductivity in Dirac semimetals and demonstrate that the odd-frequency or the Berezinskii pairing can naturally appear in these materials because of the chirality degree of freedom. We show that repulsive frequency-dependent interactions favor the Berezinskii pairing while an attractive electron-electron interaction allows for the BCS pairing. In the case of compensated Dirac and Weyl semimetals, both the conventional BCS and odd-frequency Berezinskii pairings require critical coupling. Since these pairings could originate from physically different mechanisms, our findings pave the way for controlling the realization of the Berezinskii superconductivity in topological semimetals. We also present the density of states with several cusp-like features that can serve as an experimentally verifiable signature of the odd-frequency gap.