Majorana zero modes in the hopping-modulated one-dimensional $p$-wave superconducting model

TL;DR

This paper explores how periodic hopping modulation in a one-dimensional p-wave superconductor affects Majorana zero modes, revealing dependence on modulation period and chemical potential, with distinct topological properties from potential-modulated models.

Contribution

It introduces a novel analysis of Majorana zero modes in a hopping-modulated p-wave superconductor, highlighting the impact of modulation period and chemical potential on topological phases.

Findings

Odd period modulation allows at most one MZM.

Even period modulation can host zero, one, or two MZMs.

MZMs disappear as chemical potential varies.

Abstract

We investigate the one-dimensional $p$-wave superconducting model with periodically modulated hopping and show that under time-reversal symmetry, the number of the Majorana zero modes (MZMs) strongly depends on the modulation period. If the modulation period is odd, there can be at most one MZM. However if the period is even, the number of the MZMs can be zero, one and two. In addition, the MZMs will disappear as the chemical potential varies. We derive the condition for the existence of the MZMs and show that the topological properties in this model are dramatically different from the one with periodically modulated potential.