Recent experimental progress on twisted bilayer optical lattices with ultracold atoms provides a highly controllable platform for flat-band physics beyond solid-state moiré materials. While previous studies established that interlayer coupling can generate flat bands near the Dirac points of the s-orbital bands in twisted bilayer honeycomb optical lattices—thereby enabling quantum simulation of magic-angle twisted bilayer graphene—an important open question is whether higher-orbital bands can host equally rich (and possibly distinct) flat-band structures, and how their topology and geometry differ from the s-orbital Dirac-point flat bands.
Here we systematically investigate the single-particle band structures of ultracold atoms loaded into higher orbitals of a twisted bilayer honeycomb optical lattice under tunable interlayer coupling. Our results reveal that, with appropriate interlayer coupling, flat bands can also emerge (i) near other band-degeneracy points in higher-orbital bands, and (ii) near the band bottoms and band tops of the higher-orbital bands. Importantly, we identify two distinct flattening mechanisms with different coupling dependence. For degeneracy-induced flat bands, the bandwidth is minimized near a critical interlayer coupling, whereas stronger coupling restores dispersion and reduces the flatness. By contrast, flat bands forming near band bottoms or tops flatten monotonically as the interlayer coupling increases. In the deep-lattice regime, as the interlayer coupling is tuned, some higher-orbital flat bands can drift in energy across the spectrum. In particular, flat bands initially embedded in a continuum of dispersive bands may migrate toward (and eventually into) an energy gap, becoming increasingly isolated.
We also analyze the topological and geometric properties of representative flat-band subspaces using non-Abelian Wilson loops. The flat bands induced by the s-orbital Dirac points exhibit a nontrivial Wilson-loop winding, reflecting nontrivial single-particle topology. By contrast, most higher-orbital flat bands (including those near band bottoms/tops and those associated with certain higher-orbital degeneracy points) show suppressed geometric-phase effects with vanishing Wilson-loop winding and Wilson-loop phases locked near zero, indicating topologically trivial behavior within the chosen subspace. Notably, for flat bands induced by higher-orbital Dirac points, although a robust winding analogous to the s-orbital Dirac-point case is absent, the Wilson-loop phases display finite fluctuations around zero, signaling a residual non-Abelian geometric response.
These findings establish twisted bilayer honeycomb optical lattices as a versatile platform hosting multiple types of higher-orbital flat bands with distinct formation rules and topology/geometry. The demonstrated tunability of flatness, band isolation, and geometric response lays a foundation for future studies of interaction-driven strongly correlated phases and topological quantum phase transitions in ultracold-atom moiré systems.