2d Fu–Kane–Mele invariant as Wess–Zumino action of the sewing matrix

We show that the Fu–Kane–Mele invariant of the 2 d time-reversal invariant crystalline insulators is equal to the properly normalized Wess–Zumino action of the so-called sewing-matrix field defined on the Brillouin torus. Applied to 3 d , the result permits a direct proof of the known relation betwe...

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Bibliographic Details
Published in:Letters in mathematical physics 2017-04, Vol.107 (4), p.733-755
Main Author: Gawȩdzki, Krzysztof
Format: Article
Language:English
Subjects:
Complex Systems
Geometry
Group Theory and Generalizations
Mathematical and Computational Physics
Physics
Physics and Astronomy
Theoretical
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Summary:We show that the Fu–Kane–Mele invariant of the 2 d time-reversal invariant crystalline insulators is equal to the properly normalized Wess–Zumino action of the so-called sewing-matrix field defined on the Brillouin torus. Applied to 3 d , the result permits a direct proof of the known relation between the strong Fu–Kane–Mele invariant and the Chern–Simons action of the non-Abelian Berry connection on the bundle of valence states.
ISSN:0377-9017
1573-0530
DOI:10.1007/s11005-016-0922-y