Quantum band geometry in a fractional extension of the BHZ model

Abstract

We present a generalization of the Bernevig-Hughes-Zhang (BHZ) model that incorporates a fractional dispersion relation, which reduces to an effective fractional Dirac Hamiltonian in the low-energy limit. Unlike the effective model, our generalized BHZ framework retains a compact momentum space, ensuring a well-defined Brillouin zone. We investigate the impact of fractional dispersion on the quantum geometry of the bands, revealing a significant redistribution of the Berry curvature and quantum metric across the Brillouin zone. Finally, we outline potential directions for future research, with a particular focus on experimentally measurable quantities influenced by the quantum geometry of the bands.