Edge states, Majorana fermions and topological order in superconducting wires with generalized boundary conditions

TL;DR

This paper explores how generic boundary conditions affect the topological properties and Majorana edge modes in one-dimensional superconducting wires, highlighting the impact of symmetry breaking on topological protection.

Contribution

It introduces a four-parameter classification of boundary effects and analyzes their influence on topological protection and edge correlations in superconducting wires.

Findings

Particle-hole symmetry breaking leads to loss of topological protection.

Edge-to-edge quantum correlations are resilient under certain boundary conditions.

Boundary effects can be classified and controlled via four parameters.

Abstract

We study the properties of one-dimensional topological superconductors under the influence of generic boundary conditions mimicking the coupling with external environments. We identify a general four-parameters classification of the boundary effects and show that particle-hole and reflection symmetries can be broken or preserved by appropriately fixing the boundary parameters. When the particle-hole symmetry is broken, the topological protection of the edge modes is lost due to the hybridization with the external degrees of freedom (quasiparticle poisoning). We assess the robustness of the edge modes in the various regimes by considering different quantifiers of topological properties. In particular, we investigate the resilience of the long-distance, edge-to-edge quantum mutual information and squashed entanglement, measuring the nonlocal correlations of the Majorana excitations. Besides their relevance for the open dynamics of topological systems, these results may provide a useful guide to the appropriate embedding of low-dimensional topological systems on nanodevices in realistic conditions.