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

TL;DR

This paper presents a method to distinguish trivial from topological Majorana zero-energy states in nanowire junctions through phase-biased transport measurements, focusing on supercurrent susceptibility signatures that are robust against temperature variations.

Contribution

It introduces a novel approach using supercurrent susceptibility to identify topological states, highlighting the insensitivity to chemical potential and the effects of junction transparency.

Findings

Zero-frequency susceptibility signal at = is a topological signature.

Susceptibility signals are insensitive to chemical potential in the normal region.

Critical current oscillations decrease with magnetic field only in the topological phase.

Abstract

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