Parity- and Chirality-Selected Dirac Masses in Hybrid Moir\'e--1D Superlattices
We show that a hybrid moir\'e--1D superlattice gives electrical control over whether a Dirac--Dirac momentum resonance opens a charge-neutrality gap, and through which mass channel. In twisted bilayer graphene subject to a layer-dependent unidirectional scalar potential, the charge-neutrality gap is controlled by the Fourier parity of the resonance-selected dressed interlayer harmonic: odd selected harmonics gap same-chirality Dirac-cone pairs, whereas even selected harmonics gap opposite-chirality pairs. A dressed-harmonic two-cone theory shows that this rule follows from two ingredients: the selected harmonic fixes the Pauli sector of the intercone matrix, and the dressed transverse velocities fix the relative chirality of the interacting cones. Because the 1D modulation can reverse the transverse velocity of one layer, it can electrically switch the relative chirality and hence the active mass channel, e.g., turning an even resonance from gapless to gapped. Full-wave continuum miniband calculations confirm both the exact-resonance rule and a finite near-resonant gapped window with quantitative fabrication tolerances. Far away from resonance, the same dressing yields strongly anisotropic but gapless Dirac bands. Hybrid moir\'e--1D superlattices therefore provide a route to programmable mass selection in coupled Dirac systems.