Bound states and transmission antiresonances in parabolically confined cross structures: Influence of weak magnetic fields

The ballistic conductance through a device consisting of quantum wires, to which two stubs are attached laterally, is calculated assuming parabolic confining potentials of frequencies ${\omega }_w$ for the wires and ${\omega }_s$ for the stubs. As a function of the ratio ${\omega }_w/{\omega }_s$ the conductance shows nearly periodic minima associated with quasibound states forming in the stubbed region. Applying a magnetic field $B$ normal to the plane of the device changes the symmetry of the wave functions with respect to the center of the wires and leads to new quasibound states in the stubs. The presence of the magnetic field can also lead to a second kind of state, trapped mainly in the wires by the corners of the confining potentials, that yields conductance minima as well. In either case, these bound states form for weak $B$ and strong confining frequencies and thus are not edge states. Finally, we show experimental evidence for the presence of these quasibound states.