Berry phase and anomalous Hall effect in a three-orbital tight-binding Hamiltonian

Abstract

We consider the anomalous Hall (AH) state induced by interactions in a three-orbital per unit-cell model. To be specific, we consider a model appropriate for the copper-oxide lattice to highlight the necessary conditions for time-reversal breaking states which are AH states and which are not. We compare the singularities of the wave functions of the three-orbital model, which are related to the nonzero Berry curvature, and their variation with a change of gauge to those in the two-orbital model introduced in a seminal paper by Haldane. Explicit derivation using wave functions rather than the more powerful abstract methods may provide additional physical understanding of the phenomena.