Majorana and fractionally charged bound states in 1-D Rashba nanowire under spatially varying Zeeman fields

TL;DR

This paper investigates topological phase transitions in a 1-D Rashba nanowire with spatially varying Zeeman fields, revealing conditions for Majorana and fractionally charged bound states, and analyzing their properties and polarization behaviors.

Contribution

It introduces a novel analysis of topological states in Rashba nanowires with spatially varying Zeeman fields, identifying criteria for Majorana and fractional bound states formation.

Findings

Majorana bound states are favored by large Rashba coupling or weak Zeeman fields.

Fractionally charged bound states occur in overlapping gapped regions with topologically different configurations.

Zero energy bound states exhibit spin polarization perpendicular to the Rashba vector, oscillating with Zeeman phase variations.

Abstract

We study topological phase transitions in one dimensional (1-D) Rashba nanowire under a spatially varying Zeeman field when coupled to an $s$-wave superconductor substrate. We show that this system supports both Majorana bound states (MBS) and fractionally charged bound states (FBS) of Jackiw-Rebbi type. By disassembling Zeeman Hamiltonian into multiple helical components, we find that each helical component is relating to a corresponding topological region, characterized by the emergence of MBS. FBS arises in the overlapping gapped area created by any two helical components with topologically differing configuration, analogous to those formed at the knot in SSH model. We then develop a general criteria for the occurrence conditions of MBS and FBS. Our results suggest that systems with large Rashba spin orbit couple amplitude or in presence of weak Zeeman fields favor MBS, and otherwise FBS are more favorable. In the end, we demonstrate that spin components of zero energy bound states in topological phases are polarized in the plane perpendicular to Rashba vector, and the polarization oscillates with the variance of phases of the Zeeman field.