Pressure-tuned superflat bands and electronic localization in twisted bilayer graphene-like materials

Electronic properties of twisted bilayer graphene-like materials can be modified substantially by manipulating twist angles, allowing for many exotic correlated phenomena. However, typical moiré flatbands holding these phenomena only appear with specific small twist angles. Here, we report a class of pressure-tuned superflat bands and localized electronic states over a wide range of twist angles, beyond the physics of twisted bilayer graphene near the Fermi energy. Under the slowly varying lattice distortion approximation, localized electronic states deterministically emerge in isolation at the edge of bulk spectra and are spatially centered around the AA stacked region, governed by macroscopic effective potential wells of moiré superlattices. Moreover, as macroscopic effects, pressure-tuned superflat bands and localized electronic states exhibit excellent stability against small perturbations. Our results suggest that applying pressure in generic twisted bilayer graphene-like materials may evoke widespread electronic correlations, providing opportunities for exploring electronic interactions and superconductivity.