Abstract:
The valley degree of freedom (DOF) in crystals offers great potential for manipulating classical waves; however, few studies have investigated dispersion tuning for valley states, valley states with complex wavenumbers, or valley states in functionally gradient systems. Here, we present tunable valley phononic crystals (PCs), which are composed of 3-DOF hybrid channel-cavity cells. The PCs can realize multiple novel functionalities, including tuning dispersion relations, robustly routing surface acoustic waves (SAWs), controlling wave attenuation, and modulating group velocities. Moreover, they support valley states and Dirac cones in the complex wavenumber – frequency domain. Furthermore, they can be configured to chirped valley PCs, in which edge modes are slowed down to zero group velocity states with the energy at different frequencies accumulated at different designated locations along an interface. This work may spark future investigations of topological states with complex wavenumbers in other classical systems, or topological states in functionally gradient materials.
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