Topological aspects of generalized Harper operators
Giuseppe De Nittis, Giovanni Landi
TL;DR
This paper derives generalized TKNN-equations linking Hall conductances to Chern numbers of spectral projections in Dirac-like Harper operators, expanding topological understanding of quantum Hall systems.
Contribution
It introduces a generalized framework for TKNN-equations connecting spectral projections and topological invariants in Harper operators.
Findings
Derived generalized TKNN-equations for Dirac-like Harper operators.
Connected Chern numbers of spectral projections to Hall conductance.
Provided a geometric interpretation of the equations.
Abstract
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.
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