Magnetotransport in the presence of a longitudinal barrier: multiple quantum interference of edge states

Transport in a two-dimensional electron gas subject to an external magnetic field is analyzed in the presence of a \textit{longitudinal barrier.} We show that \textit{quantum interference of the edge states} bound by the longitudinal barrier results in a drastic change of the electron motion: the degenerate discrete Landau levels are transformed into an alternating sequence of energy bands and energy gaps. These features of the electron spectrum should result in a high sensitivity of thermodynamic and transport properties of the 2D electron gas to external fields. In particular, we predict giant oscillations of the ballistic conductance and discuss nonlinear current-voltage characteristics, coherent Bloch oscillations and effects of impurities