Introduction to topological superconductivity and Majorana fermions

This short review article provides a pedagogical introduction to the rapidly growing research field of Majorana fermions in topological superconductors.We first discuss in some detail the simplest "toy model" in which Majoranas appear, namely a one-dimensional tight-binding representation of a p-wave superconductor, introduced more than ten years ago by Kitaev.We then give a general introduction to the remarkable properties of Majorana fermions in condensed matter systems, such as their intrinsically non-local nature and exotic exchange statistics, and explain why these quasiparticles are suspected to be especially well suited for lowdecoherence quantum information processing.We also discuss the experimentally…