Resonant time-dependent magnetocurrents in a Hall bar - art. no. 073406

We study the electronic current of a two-dimensional electron system confin ed to a thin strip and subject to a perpendicular, space homogeneous but ti me oscillating magnetic field. The geometry of the field producing magnet i s chosen so that the resulting space and time dependent induced electric fi eld points along the direction of the bar. Within the framework of the semi classical Boltzmann equation we derive analytical expressions for the elect ric current density both in the longitudinal and transverse directions as a function of the magnetic field strength B-0, its oscillation frequency Ome ga, and the location of the bar center. It is found that the time dependenc e of the current density is expressed in terms of solutions of a Mathieu di fferential equation whose coefficients are functions of the time, B-0, Omeg a, and the bar confining potential strength Omega (0). As functions of thes e parameters, the solutions of the Mathieu equation are known to exhibit st able or unstable behavior which in turn imply similar results for the curre nts. Such distinct behavior yield interesting measurable physical effects. The inclusion of diluted impurities and Coulomb interelectron interaction a re considered in this context and are shown not to change these results qua litatively.