Robust Fano resonance in a topological mechanical beam

The advances in topological condensed matter physics enable the manipulation of classic waves in different ways, such as unidirectional propagation featuring the suppression of backscattering and the robustness against impurities and disorder, making it possible to endow classical phenomena with topological properties. Fano resonance, a widely spread and basic kind of resonance, features an asymmetric line shape with an ultrahigh quality factor Q that usually requires delicate designs and precise fabrication. In this work, we achieve a robust Fano mechanical resonance with topological protection by engineering band inversion of two different vibrating symmetries of a pillared beam that gives rise to dark and bright edge modes. The Fano resonance results from the constructive and destructive interferences between topological dark and bright modes. It is further demonstrated that the Fano asymmetric shape of the transmission peak and its frequency are robust against random perturbations in the pillars' position as long as the symmetry is conserved. If random perturbations break the symmetry and only band inversion is involved, the asymmetric line shape of the Fano resonance weakens until disappearing before the closure of the bulk band gap, since the excitation will couple all fundamental modes of the beam. The analysis of the robustness of Fano resonance originating from band inversion and symmetry protection reveals the nature of topological protection which can be applied to design topological high-Q resonance in sensing application.