Journal
PHYSICAL REVIEW B
Volume 83, Issue 3, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevB.83.035108
Keywords
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Funding
- NSF [DMR-0549198]
- Division Of Materials Research
- Direct For Mathematical & Physical Scien [1005838] Funding Source: National Science Foundation
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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.
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