Phononic crystals as a platform for experimental physics: The direct observation of Klein tunneling

Phononic crystals consist of periodic Mie scatterers that modulate the band structure through multi-scattering to control acoustic wave propagation. Recently, the Dirac cone dispersion of phononic crystals with triangular or hexagonal lattices has been used to demonstrate interesting physics such as topologically protected edge states and Zitterbewegung effects. In this work, we present phononic crystals with triangular lattices that can be used as a platform to directly observe Klein tunneling. Klein tunneling is an important quantum mechanical physics proposed in 1929 for high-energy electrons. Klein suggested that electrons that are accelerated to the relativistic regime will tunnel through potential barriers with 100% probability regardless the width and height of the potential barrier. However, Klein tunneling has never been directly observed in quantum mechanics and solid state physics due to the difficulties in satisfying the stringent requirements. Here, we designed phononic crystals with Dirac cone dispersion at which the phonons behave as quasi-particles in the relativistic regime. Near total transmissions of the phonons through potential barriers were measured that are independent from the width and height of the potential barrier. Our results provide the first direct observation of Klein tunneling. This work will inspire a new type of applications that uses phononic crystals as a platform for the experimental studies of wave mechanics and quantum physics.