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

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.

Squashed entanglement in one-dimensional quantum matter

“…Introduction -Identifying entanglement-based order parameters able to characterize a large variety of quantum phases and at the same time to discriminate between different forms of quantum orders has remained a major challenge in condensed matter physics for the last two decades. Among the proposed parameters, block von Neumann entropy in a bipartite systems [1][2][3] and the block entanglement spectrum [4][5][6][7] have become central tools to characterize collective behaviors, including topologically ordered phases [8][9][10][11][12][13][14][15]. In two-dimensional systems, true topological order has been identified by means of the sub-leading term to the block von Neumann entanglement entropy, the so called topological entanglement entropy (TEE) [12,16,17].…”