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In a recent pre-print, we proposed that the conduction bands (CB) in a twisted homobilayer of the transition metal dichalcogenide (TMD) MoS₂ form Moire flat Chern bands, whose nontrivial topology is generated by both Moire potential and spin-orbit couplings. At 1/2 filling we predict that electron correlations drive the system into a valley polarized (VP) state with spontaneously broken time-reversal symmetry, making it a possible platform for realizing a correlated quantum anomalous Hall (QAH) state.

Observing a quantized Hall resistance depends crucially on our ability to polarize the twisted MoS₂ sample to a single valley, as the system will naturally form domains polarized to either + or - valley; in which the Moire bands carry equal and opposite Chern number. We thus use continuum model calculations of the orbital magnetization and orbital susceptibility to understand the material's response to an external magnetic field, through the framework of a Ginzburg-Landau theory.

In the process, we reveal interesting properties of the orbital magnetic susceptibility in Chern bands, which often go overlooked in the existing literature.