# Detection of second-order topological superconductors by Josephson junctions

## TL;DR

This paper proposes a method to identify second-order topological superconductors using Josephson junctions, revealing a tunable 0-pi transition that indicates topological phase changes and enables electric control of Majorana states.

## Contribution

It introduces a novel experimental signature for SOTSs via Josephson junctions and demonstrates electric control of Majorana bound states without magnetic fields.

## Key findings

- Chemical potential tuning induces topological phase transitions.
- A stable 0-pi transition is observed in Josephson junctions.
- Electric control of Majorana states is achieved without magnetic manipulation.

## Abstract

We study Josephson junctions based on second-order topological superconductors (SOTSs) which can be realized in quantum spin Hall insulators with large inverted gap in proximity to unconventional superconductors. We find that tuning the chemical potential in the superconductor strongly modifies the induced pairing of the helical edge states, resulting in topological phase transitions. In a corresponding Josephson junction, a $0$-$\pi$ transition is realized by tuning the chemical potentials in the superconducting leads. This striking feature is stable in junctions with respect to different sizes, doping the normal region, and the presence of disorder. Our transport results can serve as novel experimental signatures of SOTSs. Moreover, the $0$-$\pi$ transition constitutes a fully electric way to create or annihilate Majorana bound states in the junction without any magnetic manipulation.