Multi-mode behavior of electron Zitterbewegung induced by an electromagnetic wave in graphene

Abstract: Electrons in monolayer graphene in the presence of an electromagnetic (or electric) wave are considered theoretically. It is shown that the electron motion is a nonlinear combination of Zitterbewegung (ZB, trembling motion) resulting from the periodic potential of graphene lattice and the driving field of the wave. This complex motion is called "Multi-mode Zitterbewegung". The theory is based on the time-dependent two-band Hamiltonian taking into account the graphene band structure and interaction with the wave. Our theoretical treatment includes the rotating wave approximation and high-driving-frequency approximation for narrow wave packets, as well as numerical calculations for packets of arbitrary widths. Different regimes of electron motion are found, depending on relation between the ZB frequency $\omega_Z$ and the driving frequency $\omega_D$ for different strengths of the electron-wave interaction. Frequencies and intensities of the resulting oscillation modes are calculated. The nonlinearity of the problem results in a pronounced multi-mode behavior. Polarization of the medium is also calculated relating our theoretical results to observable quantities. The presence of driving wave, resulting in frequencies directly related to $\omega_Z$ and increasing the decay time of oscillations, should facilitate observations of the Zitterbewegung phenomenon.