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arXiv · 1703.06308

On the construction of Wannier functions in topological insulators: the 3D case

Horia D. Cornean·Domenico Monaco
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Abstract

We investigate the possibility of constructing exponentially localized composite Wannier bases, or equivalently smooth periodic Bloch frames, for 3-dimensional time-reversal symmetric topological insulators, both of bosonic and of fermionic type, so that the bases in question are also compatible with time-reversal symmetry. This problem is translated in the study, of independent interest, of homotopy classes of continuous, periodic, and time-reversal symmetric families of unitary matrices. We identify three $\mathbb{Z}_2$-valued complete invariants for these homotopy classes. When these invariants vanish, we provide an algorithm which constructs a "multi-step" logarithm that is employed to continuously deform the given family into a constant one, identically equal to the identity matrix. This algorithm leads to a constructive procedure to produce the composite Wannier bases mentioned above.

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Horia D. Cornean, Domenico Monaco. 2017-09-15. On the construction of Wannier functions in topological insulators: the 3D case. https://doi.org/10.1007/s00023-017-0621-y

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