Search for Non-Abelian Majorana modes as a route to topological quantum computation

Majorana zero modes are fermion-like excitations that were originally proposed in particle physics by Ettore Majorana and are characterized as being their own anti-particle. In condensed matter systems Majorana zero modes occur as fractionalized excitations with topologically protected degeneracy associated with such excitations. Originally, the only candidate systems for observing Majorana zero modes were the non-Abelian  fractional quantum Hall state and chiral p-wave superconductors. Over the past decade there has been a shift in favor of semiconductor/superconductor hybrid systems as a path to Majorana modes. In this seminar, I will start by explaining the basic ideas of topological quantum computation using Majorana zero modes and the potential advantages over existing systems. I will then discuss the current experimental progress by the Microsoft and Delft groups, challenges in the field and our theoretical analysis of current devices. In different ways, both these experimental developments raise questions about the meaning of topology in short systems.  I will then provide a more detailed explanation of braiding, Majorana operators and the associated topological degeneracy.