Majorana fermions in superconductors
In 1937 Ettore Majorana theoretically discovered a special class of exotic solutions for the Dirac equation. Three-quarters of a century on, no high-energy realizations of Majorana's fermions have yet been demonstrated. Nonetheless, the past decade has seen a substantial research effort centered around the idea that one can find Majorana-like quasiparticles in superconductors and superfluids. In this talk I introduce the concept of a "Majorana fermion," and show that it is relevant for the low-energy physics of certain superconducting systems. I will provide some intuition for why superconductors are a very natural place for such a particle to appear, and then work through an explicit toy model (the "Kitaev wire") that gives a formal mathematical understanding of how Majorana quasiparticle bound states appear and how they behave.