The influence of a longitudinal magnetic field on the Coulomb drag current created in the ballistic transport regime in a quantum well by a ballistic current in a nearby parallel quantum well is investigated. We consider the case where the magnetic field is so strong that the magnetic length a(B) is smaller than the width of the well. Both in the ohmic and non-ohmic case, sharp peaks of the drag current as a function of the gate voltage or chemical potential are predicted. We study the dependence of the drag current on the voltage V across the driving wire, as well as on the magnetic field B. The fine structure of the peaks due to the electron spin is also considered. By studying the Coulomb drag one can make conclusions about the electron spectrum, g-factor and electron-electron interaction in quantum wells.
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