Shaping chaos in bilayer graphene cavities

Abstract: Bilayer graphene (BLG) cavities, where electrons are confined in finite graphene flakes, provide a suitable platform to study quantum chaotic phenomena in condensed matter systems due to the trigonal warping of the Fermi surface. Here, we investigate the effect of the misalignment between the BLG lattice and the cavity geometry, introduced by rotating the boundary relative to the lattice, which can drive the system towards chaos. Based on a tight-binding model, eigenenergy level statistics reveals that rotation leads to level repulsion following Wigner-Dyson statistics, while corresponding eigenstate analysis indicates a transition from near-integrability to spatially uncorrelated random waves. Analysis of the semiclassical ray-dynamics with the trigonal-warped dispersion unveils an ergodic phase space structure, providing a quantum-classical correspondence of the onset of chaos. These findings establish an avenue to quantum chaotic phenomena in BLG cavities with potential applications in quantum device engineering.