Crossover from Majorana edge to end states in quasi-one-dimensional p-wave superconductors

TL;DR

This paper investigates the transition of Majorana states from edges to ends in quasi-one-dimensional p-wave superconductors, revealing oscillatory topological phase changes with sample width using topological indices.

Contribution

It provides a detailed analysis of the topological phase transition in strip geometries, extending previous numerical work with phase diagrams and topological index calculations.

Findings

Majorana end states can localize at opposite ends in quasi-1D systems.

Topological properties oscillate with sample width.

Phase diagrams show the presence of Majorana modes depends on system parameters.

Abstract

In a recent work [Potter and Lee, Phys. Rev. Lett. 105, 227003 (2010)], it was demonstrated by means of numerical diagonalization that the Majorana end states can be localized at opposite ends of a sample of an ideal spinless p-wave superconductor with the strip geometry beyond the strict one-dimensional limit. Here we reexamine this issue, and study the topological quantum phase transition in the same system. We give the phase diagrams of the presence of Majorana end modes by using of $Z_{2}$ topological index. It is found that the topological property of a strip geometry will change in an oscillatory way with respect of the sample width.