Majorana modes and complex band structure of quantum wires

TL;DR

This paper investigates Majorana edge states in quantum wires through complex band structure analysis, highlighting conditions for their existence and effects of Rashba mixing in 2D systems.

Contribution

It introduces a complex band structure approach to describe Majorana edge states and analyzes boundary conditions and Rashba effects in 1D and 2D systems.

Findings

Edge states are constructed from evanescent waves.

Boundary conditions restrict the existence of edge modes.

Rashba mixing influences Majorana states in 2D systems.

Abstract

We describe Majorana edge states of a semi-infinite wire using the complex band structure approach. In this method the edge state at a given energy is built as a superposition of evanescent waves. It is shown that the superposition can not always satisfy the required boundary condition, thus restricting the existence of edge modes. We discuss purely 1D and 2D systems, focussing in the latter case on the effect of the Rashba mixing term.