Geometric Criteria for Fractional Chern Insulators

Abstract

Fractional Chern insulators (FCI) realize the physics of the fractional quantum Hall effect (FQHE) in a lattice model and the absence of a magnetic field. The FQHE manifests in Landau levels, topological flat bands with remarkably simple band geometry. Mimicking the band topology alone in the lattice requires intrinsically breaking time-reversal symmetry and guarantees the lattice-analogue of the integer quantum Hall effect known as the Chern insulator, a single-particle effect. The FQHE is a many-body effect which requires flat, topological bands and has been theorized to require so-called ideal band geometry. We will explore the role of band geometry in the manifestation of FCI phases through numerical simulations, and discuss recent issues with geometry-dependent criteria.