# Supercurrent detection of topologically trivial zero-energy states in nanowire junctions

## TL;DR

This paper demonstrates that zero-energy states in trivial nanowire junctions can be detected via a phase shift in supercurrent, providing a clear method to distinguish them from Majorana states, with implications for quantum device design.

## Contribution

The study reveals that zero-energy states in trivial phases produce a detectable $ ext{pi}$-shift in supercurrent, offering a new detection method that rules out Majorana interpretations.

## Key findings

- Zero-energy states induce a $ ext{pi}$-shift in supercurrent.
- Zero-energy states can form in trivial phases under certain conditions.
- Detection method distinguishes trivial zero-energy states from Majoranas.

## Abstract

We report the emergence of zero-energy states in the trivial phase of a short nanowire junction with strong spin-orbit coupling and magnetic field, formed by strong coupling between the nanowire and two superconductors. The zero-energy states appear in the junction when the superconductors induce a large energy shift in the nanowire, such that the junction naturally forms a quantum dot, a process that is highly tunable by the superconductor width. Most importantly, we demonstrate that the zero-energy states produce a $\pi$-shift in the phase-biased supercurrent, which can be used as a simple tool for their unambiguous detection, ruling out any Majorana-like interpretation.