Abstract
Moiré superlattices in twisted van der Waals materials provide a powerful route to reshape electronic band structures, with profound consequences for the quantum geometry and topology of stacked materials. At small twist angles, the long-period moiré pattern quenches the kinetic energy and produces isolated nearly flat bands. In small-angle twisted transition metal dichalcogenides (tTMDs), the breaking of inversion symmetry, combined with isolated flat bands and small energy gaps near the Fermi level, makes this material family an ideal platform for crossed nonlinear transport enabled by an out-of-plane oscillating electric field. We demonstrate that tTMDs host sizable crossed nonlinear Hall and dynamical Nernst effects governed by quantum-geometric quantities associated with Berry connection polarizability. At large twist angles, the physics of interlayer coupling undergoes a qualitative transition. As the scattering mechanism crosses over from intravalley to intervalley Umklapp processes, the structural chirality of the twist angle, a degree of freedom overlooked in the small-angle regime, emerges as a decisive factor. In large-angle twisted bilayer graphene, the intervalley Umklapp scattering generally opens a topologically nontrivial gap near the Dirac cones, giving rise to topological domain-wall states. Extending this mechanism to three-dimensional twisted graphite, we find that the stacking configuration of the chiral structures determines the topological phase of the system. When interface symmetry is taken into account, additional topological phases appear, including topological nodal-line phases and higher-order topological insulating phases. These results establish intervalley scattering and quantum geometry as additional mechanisms for engineering topology and nonlinear responses in twisted materials.
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