In this Tutorial, we give a pedagogical introduction to Majorana bound states (MBSs) arising in semiconducting nanostructures. We start by briefly reviewing the well-known Kitaev chain toy model in order to introduce some of the basic properties of MBSs before proceeding to describe more experimentally relevant platforms. Here, our focus lies on simple “minimal” models where the Majorana wave functions can be obtained explicitly by standard methods. In the first part, we review the paradigmatic model of a Rashba nanowire with strong spin–orbit interaction (SOI) placed in a magnetic field and proximitized by a conventional $s$-wave superconductor. We identify the topological phase transition separating the trivial phase from the topological phase and demonstrate how the explicit Majorana wave functions can be obtained in the limit of strong SOI. In the second part, we discuss MBSs engineered from proximitized edge states of two-dimensional (2D) topological insulators. We introduce the Jackiw–Rebbi mechanism leading to the emergence of bound states at mass domain walls and show how this mechanism can be exploited to construct MBSs. Due to their recent interest, we also include a discussion of Majorana corner states in 2D second-order topological superconductors. This Tutorial is mainly aimed at graduate students—both theorists and experimentalists—seeking to familiarize themselves with some of the basic concepts in the field.

中文翻译：

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半导体纳米结构中的马约拉纳束缚态

在本教程中，我们对半导体纳米结构中出现的马约拉纳束缚态 (MBS) 进行了教学介绍。我们首先简要回顾著名的 Kitaev 链玩具模型，以介绍 MBS 的一些基本属性，然后再继续描述更多实验相关的平台。在这里，我们的重点在于简单的“最小”模型，其中可以通过标准方法明确获得 Majorana 波函数。在第一部分中，我们回顾了具有强自旋轨道相互作用 (SOI) 的 Rashba 纳米线的范例模型，该纳米线放置在磁场中并通过常规方法接近$秒$-波超导体。我们确定了将平凡相与拓扑相分离的拓扑相变，并演示了如何在强 SOI 的限制下获得显式马约拉纳波函数。在第二部分中，我们讨论了从二维 (2D) 拓扑绝缘体的邻近边缘状态设计的 MBS。我们介绍了导致在质量畴壁上出现束缚态的 Jackiw-Rebbi 机制，并展示了如何利用这种机制来构建 MBS。由于他们最近的兴趣，我们还讨论了二维二阶拓扑超导体中的马约拉纳角态。本教程主要针对研究生——理论家和实验家——寻求熟悉该领域的一些基本概念。