Electron trajectories on a cylindrical surface studied by ballistic transport and quantum Hall effect measurements

Magnetotransport in a high-mobility, two-dimensional electron gas on a cylindrical surface reveal peculiarities of the electron motion due to the presence of magnetic field gradients. A negative bend resistances in cross junctions at zero magnetic field and a large anisotropy of the bend resistance at low magnetic fields indicate that part of the electrons move ballistically along trochoid-like trajectories due to the varying magnetic field along the junction. Electrons on such trajectories move with the opposite velocity as compared to the direction of conventional guided trajectories. At high magnetic fields, in the quantum Hall regime, electrons move along one-dimensional channels corresponding to Landau states, which are split off the edge into the bulk due to magnetic barriers. In addition, the so-called free-electron or ‘snake’-like trajectories are formed in such regions, where the magnetic field is directed tangentially to the cylinder. We show that the Hall resistance remains quantized even in the presence of ‘snake’-like trajectories with backwards directed electron velocity.