Zero-energy Majorana states in a one-dimensional quantum wire with charge density wave instability

TL;DR

This paper demonstrates that a one-dimensional quantum wire with strong spin-orbit interactions and a charge density wave can host zero-energy Majorana states at its ends under certain conditions.

Contribution

It reveals the formation of Majorana bound states in a 1D lattice with CDW instability influenced by magnetic field and spin-orbit coupling, supported by explicit wave function calculations.

Findings

Zero-energy Majorana states localized at wire ends.

Presence of a zero-energy peak in the density of states.

Topological regime characterized by symmetry classification.

Abstract

One-dimensional lattice with strong spin-orbit interactions (SOI) and Zeeman magnetic field is shown to lead to the formation of a helical charge-density wave (CDW) state near half-filling. Interplay of the magnetic field, SOI constants and the CDW gap seems to support Majorana bound states under appropriate value of the external parameters. Explicit calculation of the quasi-particles' wave functions supports a formation of the localized zero-energy state, bounded to the sample end-points. Symmetry classification of the system is provided. Relative value of the density of states shows a precise zero-energy peak at the center of the band in the non-trivial topological regime.