Chiral zero modes in superconducting nanowires with Dresselhaus spin-orbit coupling

TL;DR

This paper analytically investigates zero-energy modes in superconducting nanowires with Dresselhaus spin-orbit coupling, revealing conditions for their existence and showing that exact zero modes can occur in finite systems under resonance.

Contribution

It provides an analytical method to determine zero modes and their conditions in nanowires with Dresselhaus coupling, including finite system cases.

Findings

Zero modes can be analytically calculated for arbitrary parameters.

Exact zero modes exist in finite systems under resonance conditions.

The study extends understanding of topological states in superconducting nanowires.

Abstract

Using chiral decomposition, we are able to find analytically the zero modes and the conditions for such modes to exist in the Kitaev ladder model and superconducting nanowires with Dresselhaus spin-orbit coupling. As a result, we are able to calculate the number of zero modes in these systems for arbitrary given parameters in the semi-infinite limit. Moreover, we find that when suitable resonance condition is satisfied exact zero modes exist even in finite systems contrary to the common belief.