Quantum bound states in narrow ballistic channels with intersections

A quantum-mechanical calculation is made of ballistic transport in intersecting narrow channels of finite length. The two-dimensional (2D) semiconductor structure we study consists of perpendicular channels, one of which connects to two reservoirs of 2D electron gas. These reservoirs serve as emitter and collectors when a potential difference is applied. At a single intersection with infinite leads, there are generally bound states that are well localized to the intersection area. In a structure with finite leads to emitter and collector, such localized states or quantum dots give rise to resonant tunneling. We show that in narrow ballistic channels with few stubs the bound states couple to each other. Therefore, the states at the different intersections combine as split bound states. The splitting is N-fold if there are N intersections. Here we study conductance in structures containing a few crossed-bar or T-shaped junctions and focus on the splitting of the resonance conductance below the first subband threshold. We argue that our results are in qualitative agreement with recent measurements. We also consider the spatial distribution of currents and show that a complicated flow pattern with vortex structures appears at higher energies.