Carriers in a two-dimensional lattice under magnetic and electric fields -art. no. 045112

We have studied the propagation of carriers in a two-dimensional system und er the influence of magnetic and electric fields. To take into account the magnetic field we have used the Peierls substitution, and have considered t he so-called Landau gauge for the vector potential. The nature of the propa gation of the wave packet under only a magnetic field is controlled by the ratio between the magnetic flux through the unit cell to the flux quantum: alpha = Phi/Phi (0). For rational values of alpha we have obtained ballisti c propagation for sufficient long times. But for irrational alpha the wave remains localized in a definite region due to incommensurability. The inclu sion of the electric field changes this picture. In fact, when the electric field is included, the degeneracy between the on-site energies is broken a long the field direction, thus inhibiting hopping along it. while in the pe rpendicular direction to the applied field propagation is favored. This beh avior is common to both rational and irrational alpha. Finally, for certain values of the electric and magnetic fields the wave packet performs an osc illatory movement; this is the phenomenon of dynamic localization.