  We consider the problem of constructing Wannier functions for Z_2 topological
insulators in two dimensions. It is well known that there is a topological
obstruction to the construction of Wannier functions for Chern insulators, but
it has been unclear whether this is also true for the Z_2 case. We consider the
Kane-Mele tight-binding model, which exhibits both normal (Z_2-even) and
topological (Z_2-odd) phases as a function of the model parameters. In the
Z_2-even phase, the usual projection-based scheme can be used to build the
Wannier representation. In the Z_2-odd phase, we do find a topological
obstruction, but only if one insists on choosing a gauge that respects the
time-reversal symmetry, corresponding to Wannier functions that come in
time-reversal pairs. If instead we are willing to violate this gauge condition,
a Wannier representation becomes possible. We present an explicit construction
of Wannier functions for the Z_2-odd phase of the Kane-Mele model via a
modified projection scheme followed by maximal localization, and confirm that
these Wannier functions correctly represent the electric polarization and other
electronic properties of the insulator.

Mesoscale and Nanoscale Physics;Materials Science