Commensurability and quantum interference magnetotransport oscillations in a two-dimensional electron gas sandwiched by superconductors

Magnetic-field dependence of the transport properties of ballistic two-dimensional electrons in a planar superconductor–normal-conductor–superconductor structure is numerically investigated. In the circumstance where the Andreev reflection from the normal-conductor–superconductor interfaces is almost perfect, two oscillatory behaviors occur for magnetic fields higher and lower than that for the coincidence of the cyclotron diameter with the separation between the superconductors. The oscillation period for the former and latter cases is proportional to the magnetic field and inverse of the magnetic field, respectively. The low-field oscillation originates from commensurability-driven guiding of Andreev-reflected trajectories along the interfaces between the normal conductor and the superconductors. If the Andreev reflection probability is considerably less than unity, the commensurability oscillation is suppressed in amplitude and is dwarfed by additionally emerged oscillations originating from the quantum interference between the Andreev- and normal-reflected components.