Effective description of Chern insulators

Abstract

The Berry curvature in Chern insulators appears to be a non-gauge-invariant quantity and does not immediately allow local length characterization. However, in two examples of two- and three-band models that we discuss, we find high-symmetry points in the Brillouin zone that have the Berry curvature invariant under diagonal gauge transformations, and may serve as expansion points of geometrical description. On the basis of the geometrical description, in the case of the Dirac based two-band Chern insulators, we conclude that the characteristic length based on the value of the Berry curvature at the expansion point plays the role of the magnetic length in the expression for the Hall viscosity. In the case of two-band models, the characteristic "cyclotron" spin is equal to 1/2, while in the three-band kagome case this spin is likely nonquantized and nonuniversal. © 2014 American Physical Society.