Theory of collective excitations in moiré materials

The observation of fractional Chern insulators (FCIs) in moiré materials has attracted significant attention in recent years. These exotic phases of matter exhibit the fractional quantum Hall effect at zero magnetic field and host fractionally charged excitations. Experiments indicate that fractionalized phases in moiré systems differ qualitatively from their counterparts in two dimensional electron gases under strong magnetic fields, suggesting that the discrete translational symmetry imposed by the moiré superlattice can give rise to new phenomenology. While a large body of recent work has focused on understanding ground state properties of moiré FCIs, the behavior of their low-energy excitations, such as anyons and magnetorotons, remains less explored. In this talk, I will present a theory for the low-energy collective excitations--magnetorotons-- of moiré FCIs based on the single mode approximation. I will show how discrete translational symmetry qualitatively modifies the nature of collective excitations, influencing the competition between FCIs and charge density waves, and leading to experimentally observable consequences in the optical response of moiré fractionalized states. I will also discuss how the collective modes depend on the Berry curvature and deviations from the trace condition in a family of nearly ideal bands that approximate the continuum model for semiconductor moiré materials, shedding light on the robustness of FCIs in twisted MoTe₂.