Resonant tunneling via quantum bound states in a classically unbound system of crossed, narrow channels

We consider the ballistic transport of noninteracting electrons in intersecting narrow channels of finite length. The structure we study consists of two perpendicular channels, one of which connects two reservoirs of two-dimensional (2D) electrons. When a weak potential difference is applied to the 2D-electron-gas regions, ballistic transport of electrons occurs within subbands as for a single channel. In addition to the subband transport, we predict that there are sharp resonances associated with bound quantum states located at the intersection of the channels. For longer channels the conductance G associated with this kind of resonant tunneling appears to be quantized as G=2${\mathit{e}}^2$N/h, where N=1 or 2. In addition to the peaks in G associated with resonant tunneling, there are also deep ‘‘antiresonances’’ that severely distort the quantized plateaus in G obtained for a single channel.