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

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 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 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. In particular, we focus on states created in wires with smooth confinement, known in the field as a quasi-MBSs, partially-separated ABSs, non-topological MBSs, or exceptional-point MBSs in systems open to reservoirs. We examine the role of their spatial non-locality, a special property of MBS wavefunctions that, together with non-Abelian braiding, is the key to realizing topological quantum computation.

This work has been published as a review in Nature Reviews Physics 2, 575–594 (2020).