Cross-over between magnetic and electric edges in quantum Hall systems

We report on the transition from magnetic edge to electric edge transport in a split magnetic gate device which applies a notch magnetic field to a two-dimensional electron gas. The gate bias allows tuning the overlap of magnetic and electric edge wave functions on the scale of the magnetic length. Conduction at the magnetic edges, in the two-dimensional bulk, is found to compete with conduction at the electric edges until the magnetic edges become depleted. Current lines then move to the electrostatic edges as in the conventional quantum Hall picture. The conductivity was modeled using the quantum Boltzmann equation in the exact hybrid potential. The theory predicts the features of the bulk-edge crossover, in good agreement with experiment.