Observation of Ordinary and High-order van Hove Singularities in Macroscopic Non-local Metamaterials

The van Hove singularity is a prominent phenomenon in periodic systems, attributed to the presence of maxima, minima, and undulation points of bands in the energy dispersion in momentum space. In this context, we report direct observations of ordinary and high-order van Hove singularity in macroscopic vibro-elastic metamaterials, achieved through one-dimensional discrete chains with designed nonlocal interactions. One experiment identifies a new feature - a stationary inflection point on the dispersion curve, which is indicative of a second-order van Hove singularity, where waves neither propagate nor spread in metamaterials. Another experiment demonstrates a maxon-roton-like dispersion relation, in which group velocity direction changes between given frequencies, resulting in three different coexisting acoustical modes at one frequency. This study demonstrates unprecedented phenomena of wave propagation. It accomplishes the accurate tailoring of fundamental dispersion bands and enables precise manipulation of waves by metamaterials.