Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices

TL;DR

This paper investigates the transition from a topological superconductor to an Anderson localized phase in a one-dimensional incommensurate lattice, highlighting the role of disorder and topological invariants.

Contribution

It provides a combined numerical and analytical study of the phase boundary and introduces the use of the topological $Z_2$ invariant to distinguish phases in disordered systems.

Findings

Transition from topological superconductor to localized phase with increasing disorder

Presence of Majorana edge states in the topological phase

Topological $Z_2$ invariant effectively distinguishes phases

Abstract

We study the competition of disorder and superconductivity for a one-dimensional p-wave superconductor in incommensurate potentials. With the increase in the strength of the incommensurate potential, the system undergoes a transition from a topological superconducting phase to a topologically trivial localized phase. The phase boundary is determined both numerically and analytically from various aspects and the topological superconducting phase is characterized by the presence of Majorana edge fermions in the system with open boundary conditions. We also calculate the topological $Z_2$ invariant of the bulk system and find it can be used to distinguish the different topological phases even for a disordered system.