Multiferroicity and Topology in Twisted Transition Metal Dichalcogenides

Abstract: Van der Waals heterostructures have recently emerged as an exciting platform for investigating the effects of strong electronic correlations, including various forms of magnetic or electrical orders. Here, we perform an unbiased exact diagonalization study of the effects of interactions on topological flat bands of twisted transition metal dichalcogenides (TMDs) at odd integer fillings. For hole-filling $\nu_h = 1$, we find that Chern insulator phases, expected from interaction-induced spin-valley polarization of the bare bands, are quite fragile, and give way to spontaneous multiferroic order -- coexisting ferroelectricity and ferromagnetism, in presence of long-range Coulomb repulsion. We provide a simple real-space picture to understand the phase diagram as a function of interaction range and strength. Our findings establish twisted TMDs as a novel and highly tunable platform for multiferroicity, and we outline a potential route towards electrical control of magnetism in the multiferroic phase.