Wannier representation of Z 2 topological insulators

By Alexey A. Soluyanov, D. Vanderbilt. 2010

255 citations recorded by the source corpus.

We consider the problem of constructing Wannier functions for ${\mathbb{Z}}_{2}$ 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 ${\mathbb{Z}}_{2}$case. We consider the Kane-Mele tight-binding model, which exhibits both normal (${\mathbb{Z}}_{2}$-even) and topological (${\mathbb{Z}}_{2}$-odd) phases as a function of the model parameters. In the ${\mathbb{Z}}_{2}$-even phase, the usual projection-based scheme can be used to build the Wannier representation. In the ${\mathbb{Z}}_{2}$-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 ${\mathbb{Z}}_{2}$-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.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/b01189c025b65567db3feef9b78419a1db0a5292

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Maximally-localized Wannier Functions: Theory and Applications (2011, background): “…electric fields along a specific spatial direction (Giustino and Pasquarello, 2005; Giustino et al., 2003; Murray and Vanderbilt, 2009; Stengel and Spaldin, 2006a; Wu et al., 2006) or for analyzing aspects of topological insulators (Coh and Vanderbilt, 2009; Soluyanov and Vanderbilt, 2011a,b).”
Colloquium: Strong-field phenomena in periodic systems (2017, background): “In a 2D system, it can be expressed in the following general form (Bansil et al., 2016; Soluyanov and Vanderbilt, 2011) ν = 1 2π ∑ n∈occ.”