ABSTRACT - DRUM - University of Maryland

Chapter 1
Introduction
The subject of this thesis, the non-Abelian topological superconductors in
two-dimensional space, is unique in many ways: it represents the simplest possible
non-Abelian phase and the only one of the whole family of non-Abelian phases that
can be understood completely in terms of non-interacting fermions, while all other
cases require strong correlation. Although the BCS theory of superconductivity was
born almost sixty years ago and superconductors are among the most well-studied
condensed matter systems, it was only realized in 2000 that exotic non-Abelian
phases can emerge in superconductors. The non-Abelian nature manifests itself in
the unusual zero-energy excitations bound to topological defects such as vortices.
Despite the theoretical interest, the study of non-Abelian superconductors is largely
driven by a potential application to quntum computation, since non-Abelian excitations
may be exploited as the fundamental building blocks of a fault-tolerant
topological quantum computer.
The purpose of the this chapter is to give a brief but self-contained account of
the theory of non-Abelian topological superconductors. We will address the following
questions:
1. What is a topological phase and how can a superconductor be topological?
1