Oscillating sign of drag in high Landau levels

Motivated by experiments, we study the sign of the Coulomb drag voltage in a double layer system in a strong magnetic field. We show that the commonly used Fermi Golden Rule approach implicitly assumes a linear dependence of intra-layer conductivity on density, and is thus inadequate in strong magnetic fields. Going beyond this approach, we show that the drag voltage commonly changes sign with density difference between the layers. We predict that in the Quantum Hall regime the Hall and longitudinal drag resistivities are comparable. Our results are also relevant for pumping and acoustoelectric experiments.