Exceptional odd-frequency pairing in non-Hermitian superconducting systems

TL;DR

This paper demonstrates that non-Hermitian superconducting systems can host exceptional points where only odd-frequency pairing survives, revealing a novel mechanism for odd-frequency superconductivity linked to spectral degeneracies.

Contribution

The study shows that non-Hermitian superconductors can intrinsically generate odd-frequency pairing at exceptional points, a phenomenon not observed in Hermitian systems.

Findings

Exceptional points exist in non-Hermitian superconductors.

Odd-frequency pairing is generated solely by non-Hermiticity.

At exceptional degeneracies, only odd-frequency pairing remains.

Abstract

We first show the realization of exceptional points in a non-Hermitian superconducting system based on a conventional superconductor and then demonstrate that, surprisingly, the system hosts odd-frequency pairing, solely generated by the non-Hermiticity. While there is a coexistence of even- and odd-frequency pairs under general conditions, we find that the even-frequency term vanishes at the exceptional degeneracies, leaving only odd-frequency pairing. This exceptional odd-frequency pairing is directly given by the imaginary part of the eigenvalues at the exceptional points and can be measured from the spectral function. Our results thus put forward non-Hermitian systems as a powerful platform to realize odd-frequency superconducting pairing.