Resonant time-dependent magnetocurrents in a Hall bar

We study the electronic current of a two-dimensional electron system confined to a thin strip and subject to a perpendicular, space homogeneous but time oscillating magnetic field. The geometry of the field producing magnet is chosen so that the resulting space and time dependent induced electric field points along the direction of the bar. Within the framework of the semiclassical Boltzmann equation we derive analytical expressions for the electric current density both in the longitudinal and transverse directions as a function of the magnetic field strength (formula presented) its oscillation frequency (formula presented) and the location of the bar center. It is found that the time dependence of the current density is expressed in terms of solutions of a Mathieu differential equation whose coefficients are functions of the time, (formula presented) (formula presented) and the bar confining potential strength (formula presented) As functions of these parameters, the solutions of the Mathieu equation are known to exhibit stable or unstable behavior which in turn imply similar results for the currents. Such distinct behavior yield interesting measurable physical effects. The inclusion of diluted impurities and Coulomb interelectron interaction are considered in this context and are shown not to change these results qualitatively.