Inhomogeneous superconductors can host electronic excitations, known as Andreev bound states (ABSs), below the superconducting energy gap. With the advent of topological superconductivity, a new kind of zero-energy ABS with exotic qualities, known as a Majorana bound state (MBS), has been discovered. A special property of MBS wavefunctions is their non-locality, which, together with non-Abelian braiding, is the key to their promise in topological quantum computation. We focus on hybrid superconductor–semiconductor nanowires as a flexible and promising experimental platform to realize one-dimensional topological superconductivity and MBSs. We review the main properties of ABSs and MBSs, state-of-the-art techniques for their detection and theoretical progress beyond minimal models, including different types of robust zero modes that may emerge without a band-topological transition.

不均匀的超导体可以在超导能隙以下承载电子激发，称为安德列夫束缚态（ABS）。随着拓扑超导的出现，一种具有奇特性质的新型零能量ABS被发现，它被称为Majorana束缚态（MBS）。MBS波函数的一个特殊属性是它们的非局部性，再加上非阿贝尔编织，是它们在拓扑量子计算中实现前景的关键。我们将混合超导体-半导体纳米线作为实现一维拓扑超导电性和MBS的灵活而有希望的实验平台。我们将回顾ABS和MBS的主要属性，以及用于检测和了解超越最小模型的最新技术的最新技术，