Twist-angle dependent continuum models and second flat Chern bands in twisted MoTe₂ and WSe₂

Motivated by recent experimental discoveries of rich electronic phases across a wide range of twist angles in moiré transition metal dichalcogenide (TMD) homobilayers, we develop a twist-angle-dependent continuum model for twisted MoTe₂ and WSe₂. The model accounts for lattice relaxations, piezoelectric polarizations, and strain-induced vector potentials, using machine learning force fields (MLFFs). By comparing band dispersions, wave functions, and quantum geometries with large-scale density functional theory (DFT) calculations, we derive a set of continuum model parameters that vary smoothly with twist angle. Through perturbation theory analysis, we find that the emergence of a second flat Chern band in both tMoTe₂ and tWSe₂ is mainly due to the strong twist-angle dependence of the layer-antisymmetric potential and interlayer tunneling. Our developed continuum models serve as a promising basis for engineering the intertwined electronic phases driven by lattice relaxations.