Nearly ballistic transport and high magnetic-field sensitivity in a $\text{Bi}_4\text{Br}_4$ topological Josephson weak link

Abstract

Superconducting weak links with high transparency offer an appealing approach for designing compact magnetic-field sensors, as their phase-dependent Andreev bound-state (ABS) spectrum produces a strong flux-to-signal response with minimal dissipation. One way to achieve ballistic transport in the weak link is to use the edge states of topological insulators, since these states resist backscattering and provide a unique path to developing topological insulator-based weak-link devices for highly efficient magnetic-field sensing. Building on this, we propose a weak-link device using superconducting Nb electrodes and a nanoribbon of $\text{Bi}_4\text{Br}_4$ as the normal region, forming a Nb-1D (one-dimensional) $\text{Bi}_4\text{Br}_4$-Nb Josephson junction. We develop first-principles tight-binding Hamiltonians and orbital-resolved interface couplings in the Wannier basis, including spin-orbit coupling, based on density functional theory (DFT) calculations. The Eliashberg spectral function of bulk Nb, obtained via density functional perturbation theory (DFPT), indicates an electron-phonon coupling strength of 1.19 and a transition temperature of about 9 K, aligning well with conventional superconductivity in Nb. The subgap conductance is primarily influenced by Andreev processes. The ABS spectrum leads to a non-sinusoidal current-phase relation (CPR) with high forward skewness ($+$1.74) and phase sensitivity to the magnetic field. Overall, our findings suggest that the Nb-1D $\text{Bi}_4\text{Br}_4$-Nb weak link is a promising platform for on-chip superconducting magnetic sensors, compatible with scalable nanofabrication and broader development of topological-superconductor hybrid electronics.