Theory of superconductivity with non-Hermitian and parity-time reversal symmetric cooper pairing symmetry

TL;DR

This paper explores a non-Hermitian, PT-symmetric superconducting model revealing novel properties like first-order phase transitions and modified thermodynamics, expanding understanding of superconductivity beyond traditional Hermitian frameworks.

Contribution

It introduces a non-Hermitian, PT-symmetric superconducting Hamiltonian with real quasiparticle spectra and distinct phase transition behavior, advancing the theoretical understanding of non-Hermitian superconductivity.

Findings

Real quasiparticle energies occur with Hermitian or anti-Hermitian order parameters.

Non-Hermitian superconductors exhibit first-order phase transitions.

Thermodynamic properties and Meissner effect are modified in non-Hermitian case.

Abstract

Recently developed parity (P) and time-reversal (T) symmetric non-Hermitian systems govern a rich variety of new and characteristically distinct physical properties, which may or may not have a direct analog in their Hermitian counterparts. We study here a non-Hermitian, PT-symmetric superconducting Hamiltonian that possesses real quasiparticle spectrum in the PT-region of the Brillouin zone. Within a single-band mean-field theory, we find that real quasiparticle energies are possible when the superconducting order parameter itself is either Hermitian or anti-Hermitian. Within the corresponding Bardeen-Cooper-Schrieffer (BCS) theory, we find that several properties are characteristically distinct and novel in the non-Hermitian pairing case than its Hermitian counterpart. One of our significant findings is that while a Hermitian superconductor gives a second order phase transition, the non-Hermitian one produces a robust first order phase transition. The corresponding thermodynamic properties, and the Meissner effect are also modified accordingly. Finally, we discuss how such a PT-symmetric pairings can emerge from an anti-symmetric potential, such as the Dzyloshinskii-Moria interaction, but with an external external bath, or complex potential, among others.