Magnetic field-induced control of transport in multiterminal focusing quantum billiards

Abstract

By exploring the four-terminal transmission of a semi-elliptic open quantum billiard in dependence of its geometry and an applied magnetic field, it is shown that a controllable switching of currents between the four terminals can be obtained. Depending on the eccentricity of the semi-ellipse and the width and placement of the leads, high transmittivity at zero magnetic field is reached either through states guided along the curved boundary or focused onto the straight boundary of the billiard. For small eccentricity, attachment of leads at the ellipse foci can yield optimized corresponding transmission, while departures from this behavior demonstrate the inapplicability of classical considerations in the deep quantum regime. The geometrically determined transmission is altered by the phase-modulating and deflecting effect of the magnetic field, which switches the pairs of leads connected by high transmittivity. It is shown that the elliptic boundary is responsible for these very special transport properties. At higher field strengths edge states form and the multiterminal transmission coefficients are determined by the topology of the billiard. The combination of magnetotransport with geometrically optimized transmission behavior leads to an efficient control of the current through the multiterminal structure.