Generalized TKNN-equations

Details Generalized TKNN-equations Generalized TKNN-equations

2011-04-06

arxiv.org/abs/1104.1214v2

Physics

Mathematical Physics

v2: 32 pages; Sect. 1 and Sect. 2.5 partially rewritten; additional minor corrections; references added. Key words: TKNN-equat

Scientific paper

We derive generalized TKNN-equations via bundle representations of the noncommutative torus with rational deformation parameter, the bundle coming from spectral projections in the torus algebra. These equations relate Chern numbers of dual bundles which we interpret as Hall conductances for Dirac-like Hamiltonians describing magnetic Bloch electrons in a strong magnetic field. We also present their generalizations for irrational values of the deformation parameter.

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