Majorana bound states in semiconducting nanostructures

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 order introduce some of basic properties MBSs before proceeding describe more experimentally relevant platforms. Here, our focus lies on simple `minimal' models where wave functions can be obtained explicitly standard methods. first part, review paradigmatic Rashba nanowire with strong spin-orbit interaction (SOI) placed magnetic field and proximitized conventional $s$-wave superconductor. identify topological phase transition separating trivial from demonstrate how explicit limit SOI. second discuss engineered edge two-dimensional (2D) insulators. Jackiw-Rebbi mechanism leading emergence at mass domain walls show exploited construct MBSs. Due their recent interest, also include discussion corner 2D second-order superconductors. This Tutorial is mainly aimed graduate students -- both theorists experimentalists seeking familiarize themselves concepts field.