Dirac electrons of a split-gate Hall bar

In this work we study several unusual properties of Klein tunneling through the abrupt and flat barriers of a split-gate Hall bar system of graphene. We show that Klein tunneling of Dirac electrons can be rather strong in such a system, and that a significant electron density can be present under the barrier. It can be shown that the probability wavefunctions for large angular momenta are identical to the probability wavefunctions of the same angular momenta in the absence of the potential barrier, i.e., it is as if the barrier does not exist and the Klein tunneling is complete. This is a unique effect in a magnetic field. We propose that STM measurements may be used to detect the presence of such a density. We have also investigated drift velocity of electrons as the center of probability wavefunction varies from outside to inside of the flat potential barrier, and find a significant deviation from the semiclassical result.