Magnon collective modes in correlated Chern insulators

Moiré materials provide a versatile platform for realizing correlated integer and fractional Chern insulators. In twisted MoTe₂, spontaneous valley polarization reduces the spin symmetry from SU(2) to Ising U(1), opening a magnon gap. Clarifying the nature of these gapped collective magnon excitations is key to understanding the stability of magnetism in correlated Chern insulators.

We develop an analytical theory that generalizes the single-mode approximation (SMA) to capture low-energy magnon excitations. Our theory closely matches exact calculations in MoTe2 and yields a transparent interpretation of the lowest-energy magnon modes as a set of symmetry-allowed local spin-flip modes. In particular, we show that the magnon gap is controlled by the interplay between the symmetry-constrained topology of the magnon wavefunctions and the topology of the underlying electronic bands.

To complement the results in MoTe2, we analytically solve more simplified Hubbard models, allowing us to (i) understand why SMA yields such a good description of the low-energy modes and pinpoint limits where it becomes exact, and (ii) derive simple relations linking the magnon gap to the Chern number and to the Berry curvature of the electronic bands.

Our results provide a unified and rigorous picture of how topology and symmetry govern the magnetic stability of correlated Chern insulators.