Periodic electron oscillation in coupled two-dimensional lattices

Abstract

We study the time evolution of electron wavepacket in the coupled two-dimensional (2D) lattices with mirror symmetry, utilizing the tight-binding Hamiltonian framework. We show analytically that the wavepacket of an electron initially located on one atomic layer in the coupled 2D square lattices exhibits a periodic oscillation in both the transverse and longitudinal directions. The frequency of this oscillation is determined by the strength of the interlayer hopping. Additionally, we provide numerical evidence that a damped periodic oscillation occurs in the coupled 2D disordered lattices with degree of disorder W, with the decay time being inversely proportional to the square of W and the frequency change being proportional to the square of W, which is similar to the case in the coupled 1D disordered lattices. Our numerical results further confirm that the periodic and damped periodic electron oscillations are universal, independent of lattice geometry, as demonstrated in AA-stacked bilayer and tri-layer graphene systems. Unlike the Bloch oscillation driven by electric fields, the periodic oscillation induced by interlayer coupling does not require the application of an electric field, has an ultrafast periodicity much shorter than the electron decoherence time in real materials, and can be tuned by adjusting the interlayer coupling. Our findings pave the way for future observation of periodic electron oscillation in material systems at the atomic scale.