Topological aspects of band theory

In this book questions that arise in the context of band theory in the presence of topologically non-trivial bands are addressed. Part of the book is aimed at the actual determination of the presence of non-trivial band topology. We develop a method to distinguish an ordinary insulator from a topological one in the presence of time-reversal symmetry. The method is implemented within the density functional theory framework and is illustrated with applications to real materials in ab initio calculations. Another question considered in this book is that of a real-space representation of topological insulators, and in particular, the construction of Wannier functions - localized real-space wavefunctions - in the presence of non-trivial band topology.