Circular bends in electron waveguides

Abstract

We study the scattering properties of bends in two-dimensional electron waveguides. We focus on a circular bend model in which the shape of the bend is determined by the bending angle and the ratio between the internal radius and the width of the asymptotic perfect leads. Such a geometry is assumed to be delimited by hard-wall boundaries. The transmission probability between the various incoming and outgoing transverse modes is studied as a function of the electron energy and the bend geometry. The total transmission probability is practically unity except at energies very close to the mode propagation thresholds. The span of the energy intervals where reflection is finite increases with the bend internal curvature. A circular bend can be a powerful mode convertor, as revealed by the rich structure of the mode-resolved transmission probabilities, which are periodic or quasiperiodic functions of the bending angle and display decaying oscillations as a function of the radius. We also show that one or more bound states exist in a circular bend and calculate their binding energy for various bend geometries. A brief discussion of the analogy between electron and electromagnetic waveguides is provided.