Title: Collective Modes and Phase Competition in Correlated Chern Insulators

Abstract: The fractional Chern insulators observed in moiré materials are believed to arise from a parent Chern band at integer filling. This band must spontaneously magnetize and valley-polarize, breaking the U(1) Ising symmetry in MoTe2 and full SU(2) spin symmetry in rhombohedral graphene superlattices. These differences in symmetry have fundamental effects on the magnon, which is gapped in the Ising case and dispersive in the SU(2) case. We develop an analytical theory of the collective modes generalizing the single-mode approximation in the Hubbard limit, which we use to compute, respectively, the gap and stiffness that set the Curie temperature of the Chern insulator. We find that the Ising gap provides a direct measure of time-reversal breaking in the ground state, whereas the spin stiffness is related to a generalized quantum metric not yet introduced in the literature. We apply these theories to MoTe2 and aligned tetra-layer graphene experiments. Finally, we discuss recent pentalayer and hexalayer graphene experiments where we argue that the parent Chern band arises from beyond mean-field correlations, providing an intrinsically different starting point than the quantum Hall system.

Lunch will be provided at 12:0 PM in EQuad J401.