Title: Crystalline Soda Can Metamaterial exhibiting Graphene-like Dispersion at subwavelength scale,
Abstract: Graphene, a honeycomb lattice of carbon atoms ruled by tight-binding
interaction, exhibits extraordinary electronic properties due to the presence
of Dirac cones within its band structure. These intriguing singularities have
naturally motivated the discovery of their classical analogues. In this work,
we present a general and direct procedure to reproduce the peculiar physics of
graphene within a very simple acoustic metamaterial: a double lattice of soda
cans resonant at two different frequencies. The first triangular sub-lattice
generates a bandgap at low frequency, which induces a tight-binding coupling
between the resonant defects of the second Honeycomb one, hence allowing us to
obtain a graphene-like band structure. We prove the relevance of this approach
by showing that both numerical and experimental dispersion relations exhibit
the requested Dirac cone. We also demonstrate the straightforward monitoring of
the coupling strength within the crystal of resonant defects. This work shows
that crystalline metamaterials are very promising candidates to investigate
tantalizing solid-state physics phenomena with classical waves.