From Andreev to Majorana bound states in hybrid superconductor-semiconductor nanowires

TL;DR

This paper reviews the properties and detection methods of Andreev and Majorana bound states in hybrid superconductor-semiconductor nanowires, highlighting their potential for topological quantum computing.

Contribution

It provides a comprehensive overview of the transition from Andreev to Majorana bound states in nanowires, including recent theoretical and experimental advances.

Findings

Majorana bound states can emerge without a topological phase transition.

Spin-orbit coupling and Zeeman field induce the transition from ABSs to MBSs.

Spatial non-locality of MBS wavefunctions is crucial for topological quantum computation.

Abstract

Electronic excitations above the ground state must overcome an energy gap in superconductors with spatially-homogeneous s-wave pairing. In contrast, inhomogeneous superconductors such as those with magnetic impurities or weak links, or heterojunctions containing normal metals or quantum dots, can host subgap electronic excitations that are generically known as Andreev bound states (ABSs). With the advent of topological superconductivity, a new kind of ABS with exotic qualities, known as Majorana bound state (MBS), has been discovered. We review the main properties of ABSs and MBSs, and the state-of-the-art techniques for their detection. We focus on hybrid superconductor-semiconductor nanowires, possibly coupled to quantum dots, as one of the most flexible and promising experimental platforms. We discuss how the combined effect of spin-orbit coupling and Zeeman field in these wires triggers the transition from ABSs into MBSs. We show theoretical progress beyond minimal models in understanding experiments, including the possibility of different types of robust zero modes that may emerge without a band-topological transition. We examine the role of spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.