Appearance of Odd-Frequency Superconductivity in a Relativistic Scenario

TL;DR

This paper demonstrates that odd-frequency superconductivity can naturally emerge in relativistic systems when viewed from different inertial frames, revealing a dynamic origin linked to Lorentz transformations.

Contribution

It introduces a relativistic model showing how odd-frequency pairing arises dynamically through Lorentz boosts in a Dirac-based superconductor.

Findings

Odd-frequency pairing appears under Lorentz boosts.

Relativistic Green functions exhibit odd-frequency components.

The work suggests intrinsic odd-frequency pairing in relativistic superconductors.

Abstract

Odd-frequency superconductivity is an exotic superconducting state in which the symmetry of the gap function is odd in frequency. Here we show that an inherent odd-frequency mode emerges dynamically under application of a Lorentz transformation of the anomalous Green function with the general frequency-dependent gap function. To see this, we consider a Dirac model with quartic potential and perform a mean-field analysis to obtain a relativistic Bogoliubov-de Gennes system. Solving the resulting Gor'kov equations yields expressions for relativistic normal and anomalous Green functions. The form of the relativistically invariant pairing term is chosen such that it reduces to BCS form in the non-relativistic limit. We choose an ansatz for the gap function in a particular frame which is even-frequency and analyze the effects on the anomalous Green function under a boost into a relativistic frame. The odd-frequency pairing emerges dynamically as a result of the boost. In the boosted frame the order parameter contains terms which are both even and odd in frequency. The relativistic correction to the anomalous Green function to first order in the boost parameter is completely odd in frequency. This work provides evidence that odd-frequency pairing may form intrinsically within relativistic superconductors.