Does Non-Hermitian superconductivity make sense?

For real world problems, we either consider Hermitian Hamiltonians, or include its Hermitian conjugate. Recently, a new class of non-Hermitian Hamiltonians is studied which are invariant under parity (P), and time-reversal (T) symmetries (or equivalent symmetries), and give real eigenvalues and unitary eigenstates. We study a non-Hermitian, PT-symmetric superconducting Hamiltonian that possesses real quasiparticle spectrum and unitary Bogoluybov states. We find that real quasiparticle energies are possible when the superconducting order parameter itself is either Hermitian or anti-Hermitian. Within the corresponding BCS theory, we find that several properties are characteristically distinct and novel in the non-Hermitian pairing case than its Hermitian counterpart. For example, anti-Hermitian pairing produces a robust first order phase transition. Finally, we discuss how such a PT -symmetric pairing can emerge from an anti-symmetric potential, such as the Dzyloshinskii-Moriya interaction, but with an external bath, or complex potential, among others. [1] A. Ghatak, T. Das, arXiv:1708.09108.