Flatbands from bound states in the continuum for orbital angular momentum localization.

Abstract

Flatband materials exhibit energy bands with zero dispersion, allowing wavefunctions to be compactly localized on the scale of a unit cell. However, such compact localization does not generally apply to wavefunctions with complex structures, such as those carrying orbital angular momentum (OAM). This limitation arises from the fact that a Bloch wavefunction consists of a plane wave factor e^ik⋅r multiplied by a periodic function u(r). While a flatband flattens the dispersion of the plane wave factor, the compact localization of a general wavefunction additionally requires a highly degenerate periodic function to accommodate its internal structure. Here, we introduce a general framework for constructing such highly degenerate flatbands by leveraging bound states in the continuum (BICs). We experimentally demonstrate this framework in two- and three-dimensional (2D and 3D) acoustic crystals, realizing flatbands with four-fold and twelve-fold degeneracy, respectively. The resulting internal degrees of freedom enable the compact localization of complex structured fields with OAM in both 2D and 3D. Our results not only establish a viable platform for OAM-compatible flatband filtering for acoustic signal processing, but also open new avenues for the construction of topologically structured waves.