# Topological Transitions in a Model for Proximity Induced Superconductivity

## TL;DR

This paper demonstrates how interlayer tunneling in a bilayer superconductor model can induce topological phase transitions, revealing new pathways to realize topological superconductivity.

## Contribution

It introduces a simple bilayer model showing topological transitions driven by interlayer tunneling and controllable parameters, advancing understanding of proximity-induced topological phases.

## Key findings

- Transitions between trivial and non-trivial topological states identified.
- Edge-state spectra and Chern indices characterize different phases.
- Transitions can be controlled via bandwidth and gate potential.

## Abstract

Using a prototype model for proximity induced superconductivity on a bilayer square lattice, we show that interlayer tunneling can drive change in topology of the Bogoliubov quasiparticle bands. Starting with topologically trivial superconductors, transitions to a non-trivial $p_x + {\rm i} p_y$ state and back to another trivial state are discovered. We characterize these phases in terms of edge-state spectra and Chern indices. We show that these transitions can also be controlled by experimentally viable control parameters, the bandwidth of the metallic layer and the gate potential. Insights from our results on a simple model for proximity induced superconductivity may open up a new route to discover topological superconductors.