  We analyze continuous partial differential models of topological insulators
in the form of systems of Dirac equations. We describe the bulk and interface
topological properties of the materials by means of indices of Fredholm
operators constructed from the Dirac operators by spectral calculus. We show
the stability of these topological invariants with respect to perturbations by
a large class of spatial heterogeneities. These models offer a quantitative
tool to analyze the interplay between topology and spatial fluctuations in
topological phases of matter. The theory is first presented for two-dimensional
materials, which display asymmetric (chiral) transport along interfaces. It is
then generalized to arbitrary dimensions with the additional assumption of
chiral symmetry in odd spatial dimensions.
