Time-diffraction and Zitterbewegung of two-dimensional massless Dirac excitations

Abstract

We explore the dynamics of two-dimensional massless Dirac-fermions within a quantum shutter approach, which involves the time-evolution of an initial cut-off plane wave. We show that the probability density is governed by an interplay between {\it diffraction in time} and {\it Zitterbewegung} phenomena, typical of relativistic quantum shutter systems with nonzero mass. The {\it time-diffraction} appears as an oscillatory pattern in the probability density, similar to the effect predicted by Moshinsky in 1952 [Phys. Rev. \textbf{88}, 625] for Schr\"odinger free matter-waves. The {\it Zitterbewegung} manifests itself as high-frequency oscillations embedded in the time-diffraction profile. We found that these two transient effects are induced by the transverse momentum component of the incident wave, $k_y$, that acts as an effective mass of the system. Furthermore, this effective mass can be manipulated by tuning the incidence angle of the initial quantum state, which allows to control the frequencies of the transients. In particular, we demonstrate that near a normal incidence condition, the {\it Zitterbewegung} appears as a series of {\it quantum beats} in the probability density, with a beating frequency $2k_yv_F$, where $v_F$ is the Fermi velocity.