Transmission antiresonances and novel bound states in cross structures at weak magnetic fields

Abstract

The ballistic conductance through a device consisting of quantum wires connected to a stubbed cavity is calculated assuming parabolic confining potentials V w and V s of frequencies Ω w for the wires and Ω w for the stubs, respectively. As a function of ω w/ ω s the conductance shows nearly periodic minima resulting from quasibound states forming in the cavity region. Applying a magnetic field B normal to the plane of the device changes the symmetry of the wavefunctions with respect to the center of the wires and leads to new quasibound states. Qualitatively the same effect occurs when the minimum of V s is shifted with respect to that of V w. In the presence of the field B a second kind of quasibound state occurs that is trapped mainly in the wires by the corners of the confining potentials. We also find that there can be a hybridization of these two types of states. As a function of B, the dips in the conductance are similar to those observed in recent experiments on stubbed cavities and can be ascribed to resonant reflection of the electrons from these quasibound states.