Colloquium

Complex band-structure analysis and topological physics of Majorana nanowires

¹ IMEC, Kapeldreef 75, 3001 Leuven, Belgium
² KU Leuven, ESAT-MICAS, Kasteelpark Arenberg 10, 3001 Leuven, Belgium
³ Institut de Física Interdisciplinària i de Sistemes Complexos IFISC (CSIC-UIB), 07122 Palma, Spain
⁴ Departament de Física, Universitat de les Illes Balears, 07122 Palma, Spain

^a e-mail: javier.osca@imec.be

Received: 7 January 2019
Received in final form: 11 March 2019
Published online: 14 May 2019

Abstract

We review applications of complex band structure theory to describe Majorana states in nanowires and nanowire junctions. The dimensionality of the considered wires is gradually increased, from strictly 1D to quasi-1D with one and two transverse dimensions. The complex wave number analysis is applied to two main types of Majorana modes: end states in hybrid semiconductor wires and chiral edge states in hybrid wires of quantum-anomalous Hall insulators. In topological NS and NSN junctions with Majorana modes conductance oscillations and spatial distributions of density and current are described. Finally, the optical absorption in finite systems with both types of Majorana modes is considered.