Magnetorotons in Moir\'e Fractional Chern Insulators

The discovery of fractional Chern insulators (FCIs) unlocks exciting opportunities to explore emergent physical excitations arising from topological and geometric effects in novel phases of quantum matter. Here we investigate the intraband neutral excitations, namely magnetorotons, in moir\'e FCIs within twisted $\rm{MoTe}_2$ by applying the Girvin, MacDonald, and Platzman (GMP) ansatz together with the method of dynamical geometric response. We reveal the universal existence of the finite-momentum magnetorotons in moir\'e FCIs and predict their characteristic scales. Furthermore, we explore the geometric nature of magnetorotons in the long-wavelength limit, identifying their gapped chiral nature with angular momentum-2, which originates from the momentum-space incompressibility of FCIs. Utilizing the excellent tunability of moir\'e systems, we extend our analysis to other incompressible phases and uncover the dynamical properties of geometric excitations influenced by quantum phase transitions. Finally, we provide experimental proposals for detecting and advancing the study of intraband neutral excitations in moir\'e FCIs.