Engineering 1D topological phases on $p$-wave superconductors

TL;DR

This paper demonstrates how impurity engineering on 2D p-wave superconductors can create 1D topological phases with Majorana states, revealing robust topological gaps and new phase control methods.

Contribution

It introduces a novel approach to induce and analyze 1D topological phases in 2D p-wave superconductors using impurity chains, including a method to compute topological invariants.

Findings

Impurity chains support multiple topological phases and Majorana end states.

Topological gaps can be a significant fraction of the superconductor's gap.

The approach allows analysis away from the gap center.

Abstract

In this work, we study how, with the aid of impurity engineering, two-dimensional $p$-wave superconductors can be employed as a platform for one-dimensional topological phases. We discover that, while chiral and helical parent states themselves are topologically nontrivial, a chain of scalar impurities on both systems support multiple topological phases and Majorana end states. We develop an approach which allows us to extract the topological invariants and subgap spectrum, even away from the center of the gap, for the representative cases of spinless, chiral and helical superconductors. We find that the magnitude of the topological gaps protecting the nontrivial phases may be a significant fraction of the gap of the underlying superconductor.