Electron Transport in Hybrid Superconductor-Normal Metal Systems

Nanoscale superconductor-normal metal single-electron turnstile is one of the promising devices for metrological applications, such as a quantum current source. In this device, electrons are transferred one-by-one across a mesoscopic metallic island. This control of transport at the single electron level is achieved due to the Coulomb interaction of electrons on the island and the sharp energy gap of the superconducting electrodes. We investigate the main error mechanisms that place the ultimate limit on the accuracy of this device. While multi-electron tunnelling processes limit the accuracy, and are therefore detrimental to the operation of the single-electron devices in metrological application, they perform the key function in information processing applications. An example is a three-terminal Cooper-pair splitting device with a superconducting electrode tunnel coupled to two normal metal electrodes. We employ the Nambu-Gor’kov and Schwinger-Keldysh formalisms to describe the nonequilibrium transport properties of the device for arbitrary transmissions of the barriers and for a general electromagnetic environment. We derive the analytic expressions for the current and the nonlocal differential conductance, and analyze the limits of clean and dirty superconductivity.