Topological aspects of generalized Harper operators

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

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 Dipartimento di Matematica

A generalized version of the TKNN-equations computing Hall conductances for generalized Dirac-like Harper operators is derived. Geometrically these equations relate Chern numbers of suitable (dual) bundles naturally associated to spectral projections of the operators.

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

Domaines: Physique mathématique [math-ph]

Giuseppe de Nittis, Giovanni Landi. Topological aspects of generalized Harper operators. N. Mebarki and J. Mimouni. AIP Conference Proceedings, American Institute of Physics, pp.58-65, 2012, Conference proceedings of the AIP, 978-0-7354-1040-4. ⟨10.1063/1.4715400⟩. ⟨hal-00674269⟩