Berry phase and Anomalous Hall Effect in a Three-orbital Tight-binding Hamiltonian

TL;DR

This paper investigates the conditions for time-reversal symmetry breaking and the emergence of the Anomalous Hall effect in a three-orbital model relevant to Copper-Oxide lattices, emphasizing Berry curvature and wave-function singularities.

Contribution

It provides a detailed wave-function based analysis of Berry curvature and AH states in a three-orbital model, extending understanding beyond previous two-orbital models.

Findings

Identifies conditions for AH states in a three-orbital model.

Analyzes Berry curvature singularities and gauge dependence.

Highlights differences from two-orbital models.

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.