Klein tunneling of gigahertz elastic waves in nanoelectromechanical metamaterials

The Klein tunneling effect describes the transmission of a relativistic particle with normal incidence through an energy barrier. It has been observed and tested in various electronic, photonic, and phononic systems, but its potential in guiding and filtering classical waves in the ultrahigh frequency regime has not been explored. Here, we report the realization of acoustic Klein tunneling in a nanoelectromechanical metamaterial system operating at gigahertz frequencies. The piezoelectric potential profiles are obtained by transmission-mode microwave impedance microscopy, from which reciprocal-space maps are extracted. The transmission rate of normally incident elastic waves is near unity in the Klein tunneling regime and drops significantly outside this frequency range, consistent with microwave network analysis. Strong angular dependent transmission is possible by controlling the launching angle of the emitter interdigital transducer. This work broadens the horizon for exploiting high-energy-physics phenomena for practical circuit applications in both classical and quantum regimes.