Transport in MultiTerminal Normal-Superconductor Devices: Reciprocity Relations, Negative and Nonlocal Resistances, and Reentrance of the Proximity Effect

We have investigated transport in a cross-shaped two-dimensional electron gas with superconducting electrodes coupled to two opposite arms. Multiterminal resistances, measured as a function of the superconducting phase difference and the magnetic flux, are analyzed in terms of an extended Landauer-B\"uttiker transport formalism. We show that extended reciprocity relations hold. Correlations between transport coefficients are obtained from, e.g., (negative) three-terminal and nonlocal resistances. Energy spectroscopy reveals a reentrant behavior of the transport coefficients around the Thouless energy.