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We present a low-energy model describing the reconstruction of the electronicspectrum in twisted bilayers of honeycomb crystals with broken sublatticesymmetry. The resulting moir\'e patterns are classified into two families withdifferent symmetry. In both cases, flat bands appear at relatively largeangles, without any magic angle condition. Transitions between them give riseto sharp resonances in the optical absorption spectrum at frequencies wellbelow the gap of the monolayer. Owing to their chiral symmetry, twistedbilayers display circular dichroism, i.e., different absorption of left andright circularly-polarized light. This optical activity is a nonlocal propertydetermined by the stacking. In hexagonal boron nitride, sensitivity to thestacking leads to strikingly different circular dichroism in the two types ofmoir\'es. Our calculations exemplify how subtle properties of the electronicwavefunctions encoded in current correlations between the layers controlphysical observables of moir\'e materials.

Flat bands and chiral optical response of moir\'e insulators