Frequency-switchable edge modes in Miura-folded checkerboard metamaterials

Miura-ori is a space-efficient paper folding shape, characterized by its doubly corrugated geometry along two orthogonal directions. Despite the rich tunability of its geometrical properties, the design of Miura-ori to realize topological edge states is still in its infancy. In our work, by optimally adjusting the folding angle and the acute angle of the Miura-folded metamaterials, we conduct the Dirac cone engineering by inducing a double Dirac cone in the band structure. We then show the emergence of a complete band gap by breaking the intrinsic glide reflection symmetry of the Miura-ori in two distinct ways, leading to configurations with opposite topological phases labeled as the inverted and everted models. Combining these two metamaterials forms edge modes propagating along the interfaces and boundaries. Especially, we demonstrate the frequency-switchable edge modes in a Miura-folded checkerboard metamaterial consisting of the two opposite topological phases, controlling several edge routing types. The edge mode switching in Miura-folded metamaterials hold significant potentials in edge wave control and energy harvesting in origami structures.