Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2010-09-07
Phys. Rev. B 83, 035108 (2011)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
Scientific paper
10.1103/PhysRevB.83.035108
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.
Soluyanov Alexey A.
Vanderbilt David
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