Exceptional Andreev spectrum and supercurrent in p-wave non-Hermitian Josephson junctions

Abstract: We investigate the spectrum of Andreev bound states and supercurrent in a $p$-wave non-Hermitian Josephson junction (NHJJ) in one dimension. The studied NHJJ is composed of two topological $p$-wave superconductors connected by a non-Hermitian dissipative junction. Starting from the effective non-Hermitian Bogoliubov-de Gennes bulk Hamiltonian, we find that a pair of exceptional points emerge in the complex spectrum of Andreev quasi-bound states. The two exceptional points locate symmetrically with respect to phase difference $\phi=\pi$ at zero real energy. Their separation is tunable by the non-Hermitian dissipation strength. By analyzing the non-Hermitian scattering process at the junction, we explicitly demonstrate the loss of quasiparticles through the decay of scattering amplitude probabilities. Furthermore, we obtain the supercurrent directly by the inelastic Andreev reflection amplitudes, which provides a more intuitive interpretation of transport properties in NHJJs. The supercurrent varies continuously as a function of $\phi$ across the exceptional points. No enhancement of critical current is observed. We also generalize our analysis to mixed $s$-$p$ wave NHJJ.