Spectral bifurcation and anomalous supercurrent in dissipative topological insulator-based Josephson junctions

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 lies within the superconducting gap. Crucially, the characteristic zero-energy crossing shifts away from \phi=\pi <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>ϕ</mml:mi> <mml:mo>=</mml:mo> <mml:mi>π</mml:mi> </mml:mrow> </mml:math> 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.