Zero-frequency supercurrent susceptibility signatures of trivial and topological zero-energy states in nanowire junctions

Abstract We propose a method to distinguish between trivial and topological, Majorana, zero-energy states (ZESs) in both short long superconductor-normal-superconductor junctions based on Rashba nanowires using phase-biased equilibrium transport measurements. In particular, we show how the sawtooth profile of supercurrent, due Majorana oscillation suppression topological phase for sufficiently superconductor regions, leads strong signal its zero-frequency susceptibility difference ϕ = π . This is notably insensitive chemical potential normal region, while ZESs only causes signals that highly varying with potential, thus turning gating region into simple experimental control knob. Furthermore, obtain that, by tuning junction transparency, critical currents undergo reduction number oscillations as function magnetic field phase, an effect find be intimately linked non-locality. Finally, our results also hold at finite temperatures, highlighting their measurability under realistic conditions.