Electron dynamics in noncommutative geometry with magnetic field and Zitterbewegung phenomenon

Starting from a gauge-invariant Dirac Hamiltonian with noncommutativity of space sector in the presence of an external uniform magnetic field, the resulting Dirac equation has been solved for electrons and its corresponding Zitterbewegung (ZBW) phenomenon has been studied. The corresponding energy spectrum is shown to be different from previous studies wherein the non-gauge-invariant Dirac Hamiltonian has been used. The effects of noncommutativity alter the amplitude as well as the cyclotron and the ZBW frequencies of the average velocity of charge carriers. This result is contrary to previous studies wherein there was no magnetic field, and hence, neither the amplitude nor the frequency of the motion was affected. Moreover, all of the ZBW frequencies of the Landau energy levels appear in the results. Also, in weak magnetic fields, we have calculated the average velocity of charge carriers for two initially localized spin-up and spin-down cases. The plotted trajectories reveal difference between these two cases. In addition, the ZBW phenomenon has been shown that manifests itself as a circular motion whose direction is spin dependent while accompanied by the cyclotron motion.