Generalized TKNN-equations

Giuseppe de Nittis (1) , Giovanni Landi (2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 Dipartimento di Matematica

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.

Mots clés: TKNN-equations; Noncommutative torus; vector bundles; Chern numbers

Domaines: Autre [cond-mat.other]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

Giuseppe de Nittis, Giovanni Landi. Generalized TKNN-equations. Advances in Theoretical and Mathematical Physics, 2012, 16 (2), pp.505-547. ⟨hal-00584324⟩