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

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 $φ=π$ 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.

Figures (6)

• Figure 1: Schematic of a non-Hermitian planar TIJJ: A 'short' TIJJ formed by placing two bulk $s$-wave singlet superconductors on the surface of a 3DTI. A top gate and a 'lossy' metallic lead ($\mathcal{N}$) are attached at the junction ($x=0$), where the gate modifies the potential barrier via an applied voltage $V_g$ and the lead introduces dissipation due to coupling to an electron reservoir.
• Figure 2: Characteristics of the NH-TIJJ for a complex barrier ($Z_1\ne 0$, $Z_2 \ne 0$) in the tunneling limit ($\Gamma_0\ll \Delta$): (a) The real (solid lines) and imaginary (dashed lines) parts of the Andreev spectrum of the NH-TIJJ as a function of the phase difference $\phi$ plotted for different angles of incidence $\theta$ taking the imaginary barrier parameter $Z_2=0.2$. The $\phi_1$ and $\phi_2$ denote the GEPs, beyond which the real part of the spectrum exits the gap and the imaginary part of the spectrum vanishes. (b) Variation of the imaginary part of the spectrum as a function of $\phi$ and $Z_2$ for the incident angle $\theta=\pi/3$, the boundary of the dark purple region demonstrates the asymmetric gap-exit points in the spectrum. (c) The zero temperature angle-resolved current $I_{\theta}(\phi)$ plotted as a function of $\phi$ for different angles of incidence. (d) The total supercurrent $I_{\mathrm{total}}(\phi)$ as a function of $\phi$ for different barrier parameters. We have chosen the real barrier parameter $Z_1=0.4$, tunneling parameter $\gamma=0.3$ and $I_0=eN\Gamma_0/(2\hbar)$ with $N$ being the number of open channels.
• Figure 3: Characteristics of the NH-TIJJ for fixed $Z_2 = 0.2$ in the tunneling limit: Variation of the (a) imaginary part of the Andreev spectrum as a function of $Z_1$ and $\phi$, and (b) total current as a function of $\phi$ for different values of $Z_1$.
• Figure 4: Characteristics of the ordinary NH-JJ for a complex barrier ($Z_1\neq0, Z_2 \neq 0$): (a) The real (solid lines) and imaginary (dashed lines) parts of the Andreev spectrum of the 2D NH-JJ as a function of the phase difference $\phi$ plotted for different angles of incidence $\theta$ taking the imaginary barrier parameter $Z_2=0.2$. (b) Variation of the imaginary part of the spectrum as a function of $\phi$ and $Z_2$ for the incident angle $\theta=\pi/3$, the boundary of the dark purple region demonstrates the symmetric gap-exit points in the spectrum. (c) The angle-resolved current $I_{\theta}(\phi)$ plotted as a function of $\phi$ for different angles of incidence at zero temperature and $Z_2=0.2$. (d) The total supercurrent $I_{\mathrm{total}}(\phi)$ as a function of $\phi$ for different barrier parameters. Here, $I'_0=e\Delta/\hbar$ and $Z_1=0.4$.
• Figure 5: Comparison of the CPR obtained from the FT formula (Eq. (\ref{['FT_formula']})) and the ABS formula (Eq. (\ref{['ABS_CPR']})) for a complex barrier ($Z_1=0.4$ and $Z_2=0.2$): (a) Planar ordinary NH-JJ, and (b) NH-TIJJ in the strong-proximity regime.