Exciton-roton mode in moir\'e fractional Chern insulators

Abstract

Moir\'e fractional Chern insulators (FCIs) are a novel class of quantum matter that realizes fractional quantum Hall (FQH) physics in zero magnetic field and provides a platform for exploring unconventional collective excitations. Here we show that hybridization between the magneto-roton and moir\'e interband excitations gives rise to an exciton-roton mode absent in continuum FQH systems in the long-wavelength limit. Using exact diagonalization and a variational Bethe-Salpeter equation for twisted MoTe$_2$, we demonstrate that this hybridization is controlled by the quantum geometry and yields a mode that combines excitonic optical response with the characteristic FCI roton minimum. The resulting exciton-roton remains low-lying, with excitation energy below the interband transition, and acquires optical activity, leading to a double-peak spectroscopic signature. These results identify optical spectroscopy as a direct probe of collective excitations in moir\'e FCIs.