Abstract
We investigate the possibility of constructing exponentially localized composite Wannier bases, or equivalently smooth periodic Bloch frames, for three-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 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.
Original language | English |
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Journal | Annales Henri Poincare |
Volume | 18 |
Issue number | 12 |
Pages (from-to) | 3862-3902 |
Number of pages | 40 |
ISSN | 1424-0637 |
DOIs | |
Publication status | Published - Dec 2017 |