Majorana edge modes in one-dimensional Kitaev chain with staggered $p$-wave superconducting pairing

TL;DR

This paper introduces a one-dimensional Kitaev chain with staggered p-wave pairing, revealing multiple topological phases with Majorana edge modes, including a novel trivial phase hosting nonzero-energy edge states, and analyzes their properties under dissipation.

Contribution

It presents a new Kitaev chain model with staggered p-wave pairing, identifying multiple phases and edge modes, including a trivial phase with nonzero-energy edge states, expanding understanding of topological superconductors.

Findings

Topologically nontrivial phase hosts two Majorana zero modes.

A trivial phase can host four nonzero-energy edge modes.

Edge modes' properties are affected by dissipation.

Abstract

We introduce a new type of one-dimensional Kitaev chain with staggered $p$-wave superconducting pairing. We find three physical regimes in this model by tuning the $p$-wave pairing and the chemical potential of the system. In the topologically nontrivial phase, there are two Majorana zero modes localized at the opposite ends of the lattice, which are characterized and protected by nonzero topological invariants. More interestingly, we also find a regime where the system can hold four unprotected nonzero-energy edge modes in the trivial phase, which is analogous to a weak topological phase. The third regime is also trivial but holds no edge modes. The emergence of zero- and nonzero-energy edge modes in the system are analyzed by transforming the lattice model into a ladder consisting of Majorana fermions, where the competition between the intra- and inter-leg couplings leads to different phases. We further investigate the properties of edge modes under the influences of dissipation, which is represented by introducing a imaginary part in the chemical potential. Our work unveils the exotic properties induced by the staggered $p$-wave pairing and provides a new platform for further exploration of Majorana edge modes.