Topology stabilized finite-temperature ferromagnetism in twisted transition metal dichalcogenides

The role topology plays in forming and stabilizing ferromagnetism has been studied for decades. The most renowned example is the quantum Hall ferromagnetism, in which the nontrivial topology enhances the exchange interaction by forcing the electron wavefunctions to be more spread out. In this talk, I will discuss another crucial effect topology can play in stabilizing two-dimensional ferromagnetism at finite temperature. In two dimensions, the Mermin–Wagner theorem forbids any translation symmetry breaking at finite temperature, and therefore constrains the Curie temperature of most two-dimensional materials with (approximate) spin SU(2) symmetry. We show that the spin SU(2) symmetry is strongly broken in spin-orbit coupled systems with valley Chern bands, e.g. twisted transition metal dichalcogenides. In twisted homobilayer MoTe2 and WSe2, in particular, the Curie temperature can reach tens of Kelvin, as obtained from a numerical soft mode calculation based on the self-consistent Hartree-Fock ground state. The underlying mechanism can be understood as the winding energy cost of the inter-valley coherent state compared to the valley polarized state, which corresponds to the anisotropy between the in-plane ferromagnet and the out-of-plane ferromagnet. These results are consistent with the relatively high temperature quantum anomalous state observed in twisted MoTe2.