Majorana fermions in density modulated p-wave superconducting wires

TL;DR

This paper investigates the robustness of Majorana edge states in a p-wave superconducting wire with a periodically modulated chemical potential, revealing conditions for their persistence and topological phase transitions.

Contribution

It demonstrates the stability of Majorana edge states under periodic modulation and introduces a topological invariant to characterize phase boundaries.

Findings

Majorana edge states are robust against periodic modulation.

Critical modulation amplitude depends on phase shifts, with some shifts allowing infinite stability.

Zero-energy spectral peaks are robust against disorder in the topological phase.

Abstract

We study the p-wave superconducting wire with a periodically modulated chemical potential and show that the Majorana edge states are robust against the periodic modulation. We find that the critical amplitude of modulated potential, at which the Majorana edge fermions and topological phase disappear, strongly depends on the phase shifts. For some specific values of the phase shift, the critical amplitude tends to infinity. The existence of Majorana edge fermions in the open chain can be characterized by a topological $Z_2$ invariant of the bulk system, which can be applied to determine the phase boundary between the topologically trivial and nontrivial superconducting phases. We also demonstrate the existence of the zero-energy peak in the spectral function of the topological superconducting phase, which is only sensitive to the open boundary condition but robust against the disorder.