Crystalline Metamaterials for Topological Properties at Subwavelength Scales

Condensed matter physics has been a continuous source of inspiration for wave physicists, due to the strong analogies between electronic propagation in solids and waves interacting with materials. Recently, in this domain, a broad field of research has emerged with the discovery that topology can play a major role in the electronic properties of materials. An exciting example can be found in the context of topological insulators, which support conductive states at their edges while no propagation is allowed within their bulk. The concept has naturally inspired the discovery of their classical analogs, with the appearance of photonic or phononic topological insulators. Yet all these proposals, which rely on photonic or phononic crystals and waveguide arrays, are inherently physically wavelength scaled, which seriously limits any application where compactness is required. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices in order to shape the way they act on waves, akin to atoms in crystals. Specifically, we prove that despite their very subwavelength typical spatial scales that usually implies to disregard their structuration, metamaterials can acquire very complex topological crystalline properties when spatially ordered. We verify unambiguously our findings in the microwave domain using quarter-wavelength-resonators, by mapping the frequency dependent fields supported by a trivial metamaterial, a topological one, and an interface between both that supports guided and robust modes. Our approach gives a straightforward tabletop platform for the study of intriguing physics that is very tedious to observe in solid state physics, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.