# Majorana Zero Modes Protected by Hopf Invariant in Topologically Trivial Superconductors

## TL;DR

This paper demonstrates that Majorana zero modes can exist in topologically trivial superconductors through a model based on the Hopf invariant, challenging the conventional association with topological phases.

## Contribution

It introduces a minimal single-band model showing Majorana zero modes in trivial superconductors using the Hopf map and invariant.

## Key findings

- Majorana zero modes can exist without topological order
- The Hopf invariant protects zero modes in trivial phases
- New avenues for realizing Majorana modes in superconductors

## Abstract

Majorana zero modes are usually attributed to topological superconductors. We study a class of two-dimensional topologically trivial superconductors without chiral edge modes, which nevertheless host robust Majorana zero modes in topological defects. The construction of this minimal single-band model is facilitated by the Hopf map and the Hopf invariant. This work will stimulate investigations of Majorana zero modes in superconductors in the topologically trivial regime.