Shape effects on scattering in quantum wires with a transverse magnetic field

We investigate the effects of the shape of the cross section of a three-dimensional quantum wire on electron scattering from a single-point impurity, in the presence of a transverse magnetic field. Assuming parabolic confining potential of frequencies ${\omega }_x$ and ${\omega }_y,$ it is shown that a magnetic field oriented along the small axis of the cross section of the wire produces the strongest effect on the conductance through the impurity (that is, the conductance is greatly enhanced). In the opposite case, it is shown that a magnetic field oriented along the large axis of the cross section of the wire produces the weakest effect (that is, the conductance is suppressed). The influence of the cross-sectional shape on the conductance versus the strength of the magnetic field is also considered and a magnetic blockade of electron transmission through the impurity is demonstrated. We further show that as the cross-sectional shape of the wire becomes asymmetric (i.e., as s increases, where $s={\omega }_y/{\omega }_x),$ switching of the conductance to different levels occurs. We use the Lippmann-Schwinger equation in order to calculate analytically the transmission coefficients.