Twisted moir\'e Dirac systems enable powerful miniband engineering but are largely fixed once the twist angle is set, whereas unidirectional (1D) electrostatic superlattices offer continuous control of Dirac anisotropy; yet robust single-particle gaps at charge neutrality are generally difficult to obtain in either setting. Here we show that combining the two into a hybrid moir\'e--1D superlattice provides a gate-defined configuration space that hosts both gap-opening resonances and strongly anisotropic gapless regimes. Using full-wave continuum miniband calculations for twisted bilayer graphene, we map the charge-neutrality-point (CNP) gap versus the 1D wavevector G1D and identify a Dirac--Dirac resonance condition. At resonance, a single-particle CNP gap emerges from a parity--chirality selection rule for the resonant inter-cone coupling, which can be electrically reprogrammed by layer-asymmetric modulation that switches the relative chirality and the active mass channel. The insulating phase persists within a finite near-resonant window, providing quantitative fabrication tolerances, while off-resonant settings remain gapless but enable strong suppression of the transverse Dirac velocity and continuous anisotropic band renormalization. Hybrid moir\'e--1D superlattices thus provide a practical route to programmable Dirac minibands and electrically selectable mass channels in coupled Dirac systems.
@article{arxiv.2603.00862,
title = {Programmable Dirac masses in hybrid moir\'e--1D superlattices},
author = {Hanzhou Tan and Pilkyung Moon},
journal= {arXiv preprint arXiv:2603.00862},
year = {2026}
}