Directly layer-resolved observation of flat-band in phononic magic-angle twisted bilayer graphene

In recent years, twistronics has gradually become an exciting upsurging topic. Among them, with the flat bands of the quasiparticle excitations, magic-angle twisted bilayer graphene can lead to exotic phenomena, including superconductivity, Mott insulating phases, and topological-related states. Many phenomena have been experimentally observed in magic-angle twisted bilayer graphene. However, the microscopic and layer-resolved excitations within the flat bands are still not directly probed. Such excitation is critical to provide a direct understandings of the coherent coupling between the two layers with subtle interlayer interactions, which is technically limited in condensed matter systems due to the lack of minimally invasive probes between the two layers of material, e.g., graphene. Here, by utilizing a phononic analog of magic-angle twisted bilayer graphene (PTBG), we directly measure excitations of each layer at the magic twist angle, enabling in situ layer resolution of the flat-band behavior. Supported by theoretical modeling, our layer-resolved measurement provides a direct understanding and interpretation of the perturbations inside the PTBG system. In magic-angle PTBG, the perturbation created by interlayer coupling is significant and highly nontrivial, strongly reshaping the low-energy states of each layer. In large-angle PTBG, low-energy states are only mildly affected by the moiré effect and can be approximated as two decoupled Dirac cones from individual layers. This work extends twistronics to artificial crystals and provides new approaches to investigate fundamental physics.