Alexey A. Soluyanov, David Vanderbilt
We develop a technique for constructing Bloch-like functions for 2D
Z_2-insulators (i.e., quantum spin-Hall insulators) that are smooth functions
of k on the entire Brillouin-zone torus. As the initial step, the occupied
subspace of the insulator is decomposed into a direct sum of two "Chern bands,"
i.e., topologically non-trivial subspaces with opposite Chern numbers. This
decomposition remains robust independent of underlying symmetries or specific
model features. Starting with the Chern bands obtained in this way, we
construct a topologically non-trivial unitary transformation that rotates the
occupied subspace into a direct sum of topologically trivial subspaces, thus
facilitating a Wannier construction. The procedure is validated and illustrated
by applying it to the Kane-Mele model.
View original:
http://arxiv.org/abs/1201.5356
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