​​Landau Level Quantization in Acoustic Rippled Graphene

Atomic lattices hosting electronic flat bands give rise to strong electron correlations and novel emergent phases. However, the discovery of flat-band quantum materials is costly and slow, while the use of acoustic metamaterials to prototype flat-band lattices is an efficient alternative approach. While the flat bands generated by twisted bilayer graphene have already been reproduced in acoustic metamaterials [1], the flat bands emerging from strain-induced Landau levels in buckled graphene [2] have not been explored in a classical system. Acoustic metamaterial graphene under a triaxial strain gauge produces a uniform pseudo-magnetic field and corresponding Landau levels. Here, we study a graphene lattice of air cavities in 3D-printed plastic under alternating pseudo-magnetic field. Specifically, we present COMSOL simulations and experimental images of the Landau levels and the quantum-Hall-like edge states. We reproduce the expected switching of sub-lattice polarization at zeroth Landau level as well as the linear dependence of the Landau level spacing that has been reported in quantum graphene.

[1] Gardezi et al, 2D Materials 8, 031002 (2021)

[2] Mao et al, Nature Physics 584, 215 (2020)