Dirac degeneracy and elastic topological valley modes induced by local resonant states

In elastic systems, the current technique to produce Dirac degeneracy is based on Bragg scattering eigenstates, which, however, suffers from operating only at relatively high frequency determined by lattice constant. Here, an elastic metamaterial plate that presents an analog to the quantum valley Hall effect (QVHE) is proposed to achieve Dirac degeneracy with local resonant states, enabling us to tune the operating frequency without altering the lattice. By introducing resonator pair into a hexagonal lattice, a local resonance states-induced Dirac cone is produced right below the local resonant band gap caused by the resonator pair. After gapping the Dirac cone with unequal masses of the resonator pair, a new local resonant band gap supporting topological edge modes immune to backscattering appears. This band gap is formed by mixing effective negative mass effect and Bragg scattering effect due to large virtual mass. These ideas are demonstrated by numerical simulation, as well as validated by the experiment on flexural wave in a textured plate. The proposed design provides a new degree of freedom to control elastic topological mode and paves the way to explore subwavelength elastic topological interface states.