Spectral Bifurcation and Anomalous Supercurrent in Dissipative Topological Insulator-based Josephson Junctions

TL;DR

This paper explores how dissipation affects topological insulator-based Josephson junctions, revealing spectral bifurcations, finite-lifetime Majorana states, and anomalous supercurrents, thus advancing understanding of dissipative quantum transport.

Contribution

It introduces a non-Hermitian model for dissipative topological Josephson junctions, uncovering spectral bifurcations and anomalous supercurrents caused by dissipation.

Findings

Spectral bifurcation with one branch merging into the continuum.

Majorana bound states acquire finite lifetime due to dissipation.

Observation of a non-zero supercurrent at zero phase difference.

Abstract

The interplay between topological protection and dissipation constitutes a critical frontier in the realization of hybrid quantum devices. Here, we investigate the transport signatures in a dissipative topological insulator-based Josephson junction, a platform that directly probes the competition between quantum coherence and loss. We model dissipation by coupling a `lossy' metallic lead to the junction, described effectively by a non-Hermitian Hamiltonian derived using the Lindblad formalism. We observe that the junction exhibits an asymmetric complex Andreev spectrum, where the imaginary energy component imposes a finite lifetime on the quasi-bound states. Furthermore, beyond specific phase intervals, the real component of the spectrum bifurcates: one branch merges with the continuum, while the other penetrates just below the superconducting gap. Crucially, the characteristic zero-energy crossing shifts away from $\phi=\pi$ and acquires a non-zero imaginary component; consequently, the associated Majorana bound states acquire a finite lifetime, signaling a loss of robustness against dissipation. Finally, this spectral asymmetry drives an anomalous supercurrent, manifested as a non-vanishing current at zero phase difference. Our results reveal how dissipation fundamentally reshapes superconducting transport in topological junctions, opening new directions for dissipation-engineered quantum devices.