Time-evolution patterns of electrons in twisted bilayer graphene

Abstract

We characterize the dynamics of electrons in twisted bilayer graphene by analyzing the time evolution of electron waves in an atomic lattice. We perform simulations based on a kernel polynomial technique using Chebyshev polynomials; this method does not requires any diagonalization of the system Hamiltonian. Our simulations reveal that interlayer electronic coupling induces an exchange of waves between the two graphene layers. This wave transfer manifests as oscillations of the layer-integrated probability densities as a function of time. For the bilayer case, it also causes a difference in the wavefront dynamics compared to monolayer graphene. The intralayer spreading of electron waves is irregular and progresses as a two-stage process. The first one, characterized by a well-defined wavefront, occurs in a short time---a wavefront forms instead during the second stage. The wavefront takes a hexagonlike shape with the vertices developing faster than the edges. Though the detail spreading form of waves depends on initial states, we observe localization of waves in specific regions of the moir\'e zone. To characterize the electron dynamics, we also analyze the time autocorrelation functions. We show that these quantities exhibit beating modulation when reducing interlayer coupling.