Hermitian and non-Hermitian Weyl physics in synthetic three-dimensional piezoelectric phononic beams

International audience; Recently, the evolution of the Weyl point (WP) caused by the introduction of nonhermiticity into Weyl semimetals has aroused great research interest. We consider elastic flexural wave propagation in a phononic beam containing piezoelectric materials and introduce nonhermiticity through active regulation of external circuits. Considering a synthetic parameter space constituted by the one-dimensional Bloch wave vector and two geometrical parameters, we demonstrate that a double WP (DWP) arises at the band crossing. Then we study its evolution from the hermitic to nonhermitic situation under the effect of the active piezoelectric materials. We find that the DWP in the hermitic case evolves into a Weyl degenerate line and a Weyl hollow ring as concerns the real and imaginary parts of the Weyl frequencies, respectively. The formation mechanisms of the DWPs, lines, and rings are explained through the Hamiltonian of the system. Further, we observe the changes of the DWP and degenerate line in the transmission spectra of finite structures. Finally, we discuss the synthetic Fermi arc interface states through the analysis of the reflected phase vortices. In this paper, we provide insights into the high-dimensional Hermitian and non-Hermitian physics in elastic wave systems using synthetic dimensions.