Title: Topology in time-reversal symmetric crystals,
Abstract: The discovery of topological insulators has reformed modern materials
science, promising to be a platform for tabletop relativistic physics,
electronic transport without scattering, and stable quantum computation.
Topological invariants are used to label distinct types of topological
insulators. But it is not generally known how many or which invariants can
exist in any given crystalline material. Using a new and efficient counting
algorithm, we study the topological invariants that arise in time-reversal
symmetric crystals. This results in a unified picture that explains the
relations between all known topological invariants in these systems. It also
predicts new topological phases and one entirely new topological invariant. We
present explicitly the classification of all two-dimensional crystalline
fermionic materials, and give a straightforward procedure for finding the
analogous result in any three-dimensional structure. Our study represents a
single, intuitive physical picture applicable to all topological invariants in
real materials, with crystal symmetries.