Magic-angle bilayer phononic graphene

Thanks to the recent discovery on the magic-angle bilayer graphene,\ntwistronics is quickly becom11 ing a burgeoning field in condensed matter\nphysics. This letter expands the realm of twistronics to acoustics by\nintroducing twisted bilayer phononic graphene, which remarkably also harbors\nthe magic angle, evidenced by the associated ultra-flat bands. Beyond mimicking\nquantum mechanical behaviors of twisted bilayer graphene, we show that their\nacoustic counterpart offers a considerably more straightforward and robust way\nto alter the interlayer hopping strength, enabling us to unlock magic angles (>\n3 degrees) inaccessible in classical twisted bilayer graphene. This study, not\nonly establishes the acoustical analog of twisted (magic-angle) bilayer\ngraphene, providing a testbed more easily accessible to probe the interaction\nand misalignment between stacked 2D materials, but also points out the\ndirection to a new phononic crystal design paradigm that could benefit\napplications such as enhanced acoustic emission and sensing.\n