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.
@article{arxiv.1112.6393,
title = {Berry phase and Anomalous Hall Effect in a Three-orbital Tight-binding Hamiltonian},
author = {Yan He and Joel Moore and C. M. Varma},
journal= {arXiv preprint arXiv:1112.6393},
year = {2015}
}