# A generic theory for Majorana zero modes in 2D superconductors

## TL;DR

This paper demonstrates that Majorana zero modes can exist in a broader class of 2D superconductors, including trivial ones, and are protected by an emergent invariant, expanding potential experimental realizations.

## Contribution

It reveals that non-Abelian Majorana zero modes are not limited to topological superconductors and introduces a new protection mechanism based on an emergent Chern-Simons invariant.

## Key findings

- Majorana zero modes can exist in trivial 2D superconductors.
- Protection of MZMs is linked to an emergent Chern-Simons invariant.
- Proposes experimental realization in 2D Dirac semimetals.

## Abstract

It is well known that non-Abelian Majorana zero modes (MZM) harbor at vortex cores in a $p_{x}+\text{i}p_{y}$ topological superconductor, which can be realized in a 2D spin-orbit coupled system with a single Fermi surface and by proximity coupling to an $s$-wave superconductor. Here we show that existence of non-Abelian MZMs is unrelated to the bulk topology of a 2D superconductor, and propose that such exotic modes can be resulted in much broader range of superconductors, being topological or trivial. For a generic 2D system with multiple Fermi surfaces and gapped out by superconducting pairings, we show that at least a single MZM survives if there are only odd number of Fermi surfaces of which the corresponding superconducting orders have vortices, and such MZM is protected by an emergent Chern-Simons invariant, irrespective of the bulk topology of the superconductor. This result may enrich new experimental schemes for realizing non-Aelian MZMs. In particular, we propose a minimal scheme to realize the MZMs in a 2D superconducting Dirac semimetal with trivial bulk topology, which can be well achieved based on the recent cold atom experiments.