Effects of edge disorder on the stability of quantum oscillations in two-dimensional coupled systems

This paper utilizes the theory of quantum diffusion to analyze the electron probability and spreading width of a wavepacket on each layer in a two-dimensional (2D) coupled system with edge disorder, aiming to clarify the effects of edge disorder on the stability of the electron periodic oscillations in 2D coupled systems. Using coupled 2D square lattices with edge disorder as an example, we show that, the electron probability and wavepacket spreading width exhibit periodic oscillations and damped oscillations, respectively, before and after the wavepacket reaches the boundary. Furthermore, these electron oscillations exhibit strong resistance against disorder perturbation with a longer decay time in the regime of large disorder, due to the combined influences of ordered and disordered site energies in the central and edge regions. Finally, we numerically verified the universality of the results through bilayer graphene, demonstrating that this anomalous quantum oscillatory behavior is independent of lattice geometry. Our findings are helpful in designing relevant quantum devices and understanding the influence of edge disorder on the stability of electron periodic oscillations in 2D coupled systems.