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We investigate the existence of interface states induced by broken inversionsymmetries in two-dimensional quasicrystal lattices. We introduce a 10-foldrotationally symmetric quasicrystal lattice whose inversion symmetry is brokenthrough a mass dimerization that produces two 5-fold symmetric sub-lattices. Byconsidering resonator scatterers attached to an elastic plate, we illustratethe emergence of bands of interface states that accompany a band inversion ofthe quasicrystal spectrum as a function of the dimerization parameter. Thesebands are filled by modes which are localized along domain-wall interfacesseparating regions of opposite inversion symmetry. These features drawparallels to the dynamic behavior of topological interface states in thecontext of the valley Hall effect, which has been so far limited to periodiclattices. We numerically and experimentally demonstrate wave-guiding in aquasicrystal lattice featuring a zig-zag interface with sharp turns of 36degrees, which goes beyond the limitation of 60 degrees associated with 6-foldsymmetric (i.e., honeycomb) periodic lattices. Our results provide newopportunities for symmetry-based quasicrystalline topological waveguides thatdo not require time-reversal symmetry breaking, and that allow for higherfreedom in the design of their waveguiding trajectories by leveraginghigher-order rotational symmetries.

Interface states in two-dimensional quasicrystals with broken inversion symmetry