Coherent transport through a T-shaped mesoscopic superconducting junction

We highlight a ‘‘transverse’’ interference effect, arising from the coupling between electrons and holes, induced by a superconducting island in contact with a normal metal. As an example we compute the electrical conductance G of a T-shaped mesoscopic sample, formed by joining a horizontal bar of normal metal to a vertical leg of the same material. With a superconducting island located on the vertical leg and the current flowing horizontally, we examine the dependence of G on the distance L of the island from the horizontal bar. Of particular interest is the differential conductance G(E) at an applied voltage E=eV, which due to quantum interference between electrons and Andreev reflected holes, is predicted to oscillate with both L and E. For a system with a spherical Fermi surface, the period of oscillation with E is π${\mathit{E}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{F}}$L and with L is π${\mathit{E}}_{\mathit{F}}$/${\mathit{k}}_{\mathit{F}}$E, where ${\mathit{E}}_{\mathit{F}}$ is the Fermi energy and ${\mathit{k}}_{\mathit{F}}$ the Fermi wave vector.