Quantum Geometry and Band Topology in Interacting Systems

Quantum geometry (or band geometry) and band topology describe, respectively, the local and global properties of the Bloch electron wavefunctions in quantum materials. While extensive research has been conducted on these topics at the single-particle level, the interplay between band geometry/topology and interactions is much less explored. In this talk, I will mainly cover two recent developments in this direction. First, I will discuss the significant contributions from the band geometry to the electron-phonon coupling constants in graphene and MgB₂. Then, I will talk about fractional Chern insulators (FCIs), which are induced by Coulomb interaction in fractionally filled (nearly-)flat Chern bands; FCIs have recently been observed in twisted MoTe₂ and graphene-hBN superlattices, and I will mainly address how to explain various experimental phenomena simultaneously. I will also cover other related aspects and future research directions.