Pseudomagnetic fields and Landau levels for out-of-plane elastic waves in gradient snowflake-shaped crystals

Highlights: • The pseudomagnetic fields in phononic systems can mimic giant extern driving fields through pure mechanical means. • Landau levels for elastic waves are formed near the Dirac cone region by introducing pseudomagnetic fields. • The sublattice polarized bulk states and the magnetic-induced edge states are achieved in elastic wave systems. -- Abstract: The study of pseudomagnetic fields (PMF) in classical waves draws a growing attention due to the strength of PMF far higher than real magnetic fields. Here, we show that a giant PMF for out-of-plane elastic waves can be created in the snowflake-shaped crystals by introducing a gradient angle modulation along one direction. In particular, we demonstrate that the Landau energy levels for out-of-plane elastic waves can be formed near the Dirac cone region, as a hallmark of high-field physics induced by PMF. Moreover, the sublattice polarized bulk states similar to the behavior of graphene electron in magnetic fields are achieved in our elastic systems. Furthermore, the magnetic-induced edge state propagation along bend pathway is also demonstrated. Our study provides a new paradigm for manipulating the elastic waves in aspects of information processing and energy transport.