Speaker
Description
Topological states of matter have emerged in the last decade as one of the absolute most vibrant areas of condensed matter physics. These range from topological insulators and Weyl semimetals but also an abundance of different topological states in superconductors. The defining property for all these phases of matter is a global non-trivial topology of their electronic structure. This is fundamentally different from the traditional Landau paradigm traditionally used to classify matter, where local order parameters appearing due to spontaneous symmetry breaking play the key role. Topological superconductors are particularly interesting as they automatically join these two fundamentally different views of matter having both a global topological order and a local superconducting order parameter. Combining this with the distinctive particle-hole mixing in superconductors gives rise to emergent Majorana fermion states, that can be viewed as half electron quasiparticles offering unique possibilities to realize robust quantum computation.
In these lectures I will cover the basic theory of topological superconductivity. Starting from an elementary understanding of conventional BCS superconductivity and topological insulators, I will discuss several different topological superconducting states, as well as focusing on how and why Majorana fermions appear as topological protected edge states.
