Shining Light on Collective Modes in Moiré Fractional Chern Insulators

We show that collective excitations and optical responses of moiré fractional Chern insulators (FCIs) drastically differ from those of standard fractional quantum Hall (FQH) states in a Landau level. By constructing a variational wave function that incorporates the moiré lattice effect, we capture the collective modes in FCIs across a range of crystal momenta including the roton minimum. Interestingly, new collective modes are found in the long wavelength limit (q→0) at low energy below the excitation continuum, distinct from the FQH case. Some of these modes are optically active and manifest as sharp peaks in optical conductivity at THz frequency. We further show that intraband optical absorption and spectral weight in twisted MoTe_{2} are highly tunable by the displacement field. Our Letter thus establishes optical spectroscopy as a powerful tool to illuminate the unique collective modes of moiré FCIs.