Introduction

Quasiparticle transport processes across metallic junctions play a fundamental role in the functioning of many devices used nowadays in mesoscopic physics. One such device is the single electron transistor (SET), invented and fabricated almost two decades ago [1], which has found remarkable applications as ultrasensitive charge detector [2] and as amplifier operating at the quantum limit [3]. In the emerging field of quantum computing the superconducting SET has been proposed and used as a quantum bit [4]. With advancements in lithography techniques, this device can be fully suspended [5], thus providing a new avenue for nanoelectromechanics. Similar devices are currently used (in practice arrays with several junctions turn out to provide a larger signal-to-noise ratio) as Coulomb blockade (CBT) primary thermometers [6]. Also, superconducting double-junction systems with appropriate bias can be operated as microcoolers [7]. The functioning of these three classes of devices is based on the interplay between two out of the three relevant energy scales: the superconducting gap, the charging energy, and the temperature. For example, in the case of microcoolers, the temperature and the gap are finite, and the charging energy is typically zero. A natural question to raise is then what happens if the charging energy is no longer negligible, for example if one wishes to miniaturize further these devices. In contradistinction, for CBTs the charging energy and the temperature are important, and the superconducting gap is a nuisance. A solution is to suppress the gap by using external magnetic fields, an idea which makes these temperature sensors more bulky and risky to use near magnetic-field sensitive components. Therefore, understanding the corrections introduced by the superconducting gap could provide an interesting alternative route, although, with present technology, the level of control required of the gap value could be very difficult to achieve. Finally, electrometers and superconducting SETs are operated at low temperatures, with the charging energy and the gap being dominant. However, large charging energies are not always easy to obtain for some materials due to technological limitations, while achieving effective very low electronic temperatures is limited by various nonequilibrium processes. In this article we present a unified treatment of these three devices by solving the transport problem in the most general case, when all three energy scales are present. Our goal is to give an eye guidance for the experimentalist working in the field, showing what are the main characteristics visible in the I–V s and G–V s, resulting from sequential tunneling. Both the electrical and the thermal transport are calculated in the framework of a generalized so-called ”orthodox” theory, which includes the superconducting gap. For completeness, we offer a self-consistent review of this theory, which has become nowadays the standard model for describing sequential quasiparticle transport processes in these devices. We ignore Josephson effects which, for the purpose of this analysis just add certain well-known