  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.
