Meissner effect in non-Hermitian superconductors

TL;DR

This paper explores the Meissner effect in non-Hermitian superconductors, revealing conditions for diamagnetic and paramagnetic responses, and identifying potential instabilities linked to negative superfluid stiffness.

Contribution

It provides a theoretical analysis of the Meissner effect in non-Hermitian BCS superconductors, highlighting how mean field parameters influence magnetic response and stability.

Findings

Positive real mean fields lead to diamagnetic Meissner effect in 3D s-wave superconductors.

Near anti-Hermitian mean fields, 2D superconductors can exhibit paramagnetic response.

Negative superfluid stiffness signals instability of the superconducting state.

Abstract

We study theoretically Meissner effect in non-Hermitian systems of BCS type, i.e., with an electron-electron interaction leading to the mean field description in a Cooper channel, via superfluid stiffness. We show that depending on the values of the mean fields, chemical potential, and temperature, we obtain paramagnetic or diamagnetic Meissner effect. Notably, positive real part of the product of mean fields guarantees diamagnetic Meissner effect in an $s$-wave 3D non-Hermitian superconductor. Once the mean fields are close to being anti-Hermitian, 2D $s$-, $p_x$-, and $d$-wave superconductors exhibit interesting behaviour, including negative superfluid stiffness giving paramagnetic Meissner effect for certain parameters. Negative superfluid stiffness indicates instability of this collective state.