Continuous bulk and interface description of topological insulators

We analyze the topological properties of systems of Dirac equations in the presence of heterogeneities to model transport in topological insulators. The topology is described by means of indices of Fredholm operators. We describe bulk and interface topological invariants first for two-dimensional materials, which find practical applications, and then in arbitrary dimensions. In the two-dimensional setting, we relate the interface invariant to a physical observable describing asymmetric current along the interface.