# Majorana corner flat bands in two-dimensional second-order topological superconductors

## TL;DR

This paper predicts that confining a second-order topological superconductor with a harmonic potential induces Majorana corner flat bands, arising from boundary states, which are robust and experimentally observable.

## Contribution

It introduces a novel mechanism for Majorana flat bands in second-order topological superconductors via harmonic trapping, differing from conventional origins.

## Key findings

- Majorana corner flat bands emerge under harmonic confinement.
- These flat bands originate from boundary states, not bulk gap closing.
- The transition to flat bands is a smooth crossover, robust against trap strength.

## Abstract

In this paper we find that confining a second-order topological superconductor with a harmonic potential leads to a proliferation of Majorana corner modes. As a consequence, this results in the formation of Majorana corner flat bands which have a fundamentally different origin from that of the conventional mechanism. This is due to the fact that they arise solely from the one-dimensional gapped boundary states of the hybrid system that become gapless without the bulk gap closing under the increase of the trapping potential magnitude. The Majorana corner states are found to be robust against the strength of the harmonic trap and the transition from Majorana corner states to Majorana flat bands is merely a smooth crossover. As a harmonic trap can potentially be realized in heterostructures, this proposal paves a way to observe these Majorana corner flat bands in an experimental context.