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 with zero energy locate symmetrically with respect to Josephson phase difference $\varphi =\pi$, at which a Majorana zero mode persists. Notably, the exceptional points descend from a pair of Majorana zero modes after turning on the non-Hermiticity and are topologically protected. 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 $\varphi$ across the exceptional points. No enhancement of critical current is observed. We also generalize our analysis to a mixed $s$-$p$ wave NHJJ. Our results provide new insights on transport properties of Josephson junctions in presence of Majorana zero modes, exceptional points, and non-Hermiticity.

8 pages, 4 figures; close to published version

References in corpus (14)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Quantum trajectories and open many-body quantum systems
• Fermion-parity anomaly of the critical supercurrent in the quantum spin-Hall effect
• Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport
• Non-Hermitian phase-biased Josephson junctions
• Suppressing Andreev bound state zero bias peaks using a strongly dissipative lead
• Anomalous Andreev Spectrum and Transport in Non-Hermitian Josephson Junctions
• Universal conductance scaling of Andreev reflections using a dissipative probe
• Josephson effect in a junction coupled to an electron reservoir
• Non-hermitian topology in multiterminal superconducting junctions
• Non-Hermitian multiterminal phase-biased Josephson junctions
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• Signatures of exceptional points in multiterminal superconductor-normal metal junctions

Cited by in corpus (2)

• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• Dissipation-Induced Steady States in Topological Superconductors: Mechanisms and Design Principles