Giant Flat Band Amplification via Inertial Anchors

Abstract

In electronic materials, flat bands are associated with compact electron localization, with implications for superconductivity, ferromagnetism and strongly correlated systems. The physical significance of their counterparts in elastic media is far less charted. Here we report a strategy to achieve elastic flat bands through an inertial retrofitting of classical lattice architectures. The idea is to alter the cell geometry to realize a network of inertial anchors, effectively partitioning the lattice into an array of weakly coupled emergent resonators, whose resonances appear as flat bands in the phonon spectrum. We demonstrate flat-band conditions that combine localized and extended state attributes and induce a giant response that is spatially and temporally persistent. Laser vibrometry experiments reveal three signatures of this mechanism: amplification up to two orders of magnitude compared to pass band and band gap conditions, multi-cell activation that is agnostic to the source location, and a persistent transient response even after several excitation cycles.