# Detection of second-order topological superconductors by Josephson junctions

## Date & Facts

Zhang, Song-Bo and Trauzettel, Björn, Detection of second-order topological superconductors by Josephson junctions.

## Abstract

We study Josephson junctions based on a second-order topological superconductor (SOTS) which is realized in a quantum spin Hall insulator with a large inverted gap in proximity to an unconventional superconductor. We find that tuning the chemical potential in the superconductor strongly modifies the pairing gap of the helical edge states and leads to topological phase transitions. As a result, the supercurrent in the junction is controllable and a $0$-$\pi$ transition is realized by tuning the chemical potentials in the superconducting leads. These striking features are stable in junctions with different sizes, doping in the normal region, and in the presence of disorder. We propose them as novel experimental signatures of SOTSs. Moreover, the $0$-$\pi$ transition can serve as a fully electric way to create or annihilate Majorana bound states in the junction without magnetic manipulation.

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