# Non-trivial Chern numbers in three-terminal Josephson junctions

## TL;DR

This paper demonstrates that topological phase transitions characterized by changes in Chern numbers can be controlled in three-terminal Josephson junctions using magnetic flux, extending previous predictions about four-terminal systems.

## Contribution

It introduces a new method to tune topological transitions in 3-terminal Josephson junctions via magnetic flux, expanding the understanding of topological properties in these systems.

## Key findings

- Topological transitions can be controlled with magnetic flux in 3-terminal junctions.
- Chern numbers change during these topological transitions.
- The study extends the understanding of topological phenomena from 4-terminal to 3-terminal junctions.

## Abstract

Recently it has been predicted that the Andreev bound state spectrum of 4-terminal Josephson junctions may possess zero-energy Weyl singularities. Using one superconducting phase as a control parameter, these singularities are associated with topological transitions between time-reversal symmetry broken phases with different Chern numbers. Here we show that such topological transitions may also be tuned with a magnetic flux through the junction area in a 3-terminal geometry.