  Topological insulators are a new class of materials which have gapped spectra
in the bulk, but are accompanied by topologically protected gapless excitations
at the surface (edge) of the system. These phenomena have a close relationship
with symmetry and dimensionality of the system through quantum anomalies. We
point out that such a surface state is a physical realization of the
domain-wall/overlap fermion. From this point of view, we discuss its
implications for experiments of topological insulators. We also discuss an
unconventional overlap fermion, which is suggested by the "periodic table" of
topological insulators and superconductors.
