  The topological invariant of a topological insulator (or superconductor) is
given by the number of symmetry-protected edge states present at the Fermi
level. Despite this fact, established expressions for the topological invariant
require knowledge of all states below the Fermi energy. Here, we propose a way
to calculate the topological invariant employing solely its scattering matrix
at the Fermi level without knowledge of the full spectrum. Since the approach
based on scattering matrices requires much less information than the
Hamiltonian-based approaches (surface versus bulk), it is numerically more
efficient. In particular, is better-suited for studying disordered systems.
Moreover, it directly connects the topological invariant to transport
properties potentially providing a new way to probe topological phases.
