Emergence of elastic chiral Landau levels and snake states

In this paper, we present a method for generating a synthetic gauge field in the vertical direction by linearly modulating the mass term in a Dirac equation model. This allows for the quantization of Landau levels through the generated pseudomagnetic field, with the chiral zeroth Landau level being topologically protected. An elastic snake state is realized using the coupling between the zeroth and the first Landau levels. For demonstration, our theoretical predictions are realized numerically in an elastic medium of truss structures arranged in a honeycomb lattice. Our results, supported by theory and simulations, establish a framework for generating pseudomagnetic fields in elastic systems with potential applications in waveguides and cloaking.