Meissner effect in non-Hermitian superconductors

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.