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\(2d\) Fu-Kane-Mele invariant as Wess-Zumino action of the sewing matrix. (English) Zbl 1370.53024

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 \(3d\), 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.

MSC:

53C08 Differential geometric aspects of gerbes and differential characters
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