In this book the coherent quantum transport of electrons through two-dimensional mesoscopic
structures is explored in dependence of the interplay between the confining geometry and the
impact of applied magnetic fields aiming at conductance controllability. After a top-down
insightful presentation of the elements of mesoscopic devices and transport theory a
computational technique which treats multiterminal structures of arbitrary geometry and
topology is developed. The method relies on the modular assembly of the electronic propagators
of subsystems which are inter- or intra-connected providing large flexibility in system setups
combined with high computational efficiency. Conductance control is first demonstrated for
elongated quantum billiards and arrays thereof where a weak magnetic field tunes the current by
phase modulation of interfering lead-coupled states geometrically separated from confined
states. Soft-wall potentials are then employed for efficient and robust conductance switching
by isolating energy persistent collimated or magnetically deflected electron paths from Fano
resonances. In a multiterminal configuration the guiding and focusing property of curved
boundary sections enables magnetically controlled directional transport with input electron
waves flowing exclusively to selected outputs. Together with a comprehensive analysis of
characteristic transport features and spatial distributions of scattering states the results
demonstrate the geometrically assisted design of magnetoconductance control elements in the
linear response regime.
