Z. Phys. B - Condensed Matter 85, 319-325 (1991) Condensed Zeitsehrift Matter far PhysJkB 9 Springer-Vcrlag 1991 Single charge tunneling: a brief introduction Hermann Grabert 1'2 1Fachbereich Physik, Universit/it-GH Essen, W-4300 Essen, Federal Republic of Germany 2 Service de Physique de l'Etat Condens6, Centre d'Etudes de Saclay, F-91191 Gif-sur-Yvette, France Received August 12, 1991 The field of single charge tunneling comprises of phe- nomena where the tunneling of a microscopic charge, usually carried by an electron or a Cooper pair, leads to macroscopically observable effects. The basic principles governing this area of research are briefly outlined and the present state of the art is discussed. 1. Introduction The importance of Coulomb charging effects for charge transfer through small systems was first noted several decades ago [1 5]. At that time, Coulomb blockade phe- nomena could only be observed in granular metallic ma- terials, in which single electron effects and random media properties interplay. Nowadays, modern lithography al- lows for the controlled fabrication of submicron struc- tures, where metallic islands with capacitances C in the fF range or below are separated by tunneling barriers with resistances R T well above the resistance quantum R K = h/e2~-25.8 kf~. In such systems, the charging energy Ec=e2/2 C of a single excess electron on the metallic is- land exceeds the energy kBT of thermal fluctuations at sub Kelvin temperatures. As a consequence, a Coulomb blockade of tunneling arises [6, 7] which can be exploited to transfer single charges from one island to another in a controlled way [8, 9]. The paragraph above indicates the basic requirements for Single Charge Tunneling (SCT) phenomena to occur. Leaving aside for the moment the special case of a single tunnel junction which will be discussed in the following section, these conditions are as follows. Firstly, the sys- tem must have metallic islands that are connected to oth- er metallic regions only via tunnel barriers with a tunnel- ing resistance that exceeds the resistance quantum, i.e., RT>~ R K . (1) This condition ensures that the wave function of an ex- cess electron or Cooper pair on an island is basically localized there. In systems with lower tunneling resis- tances, charges can be transferred through small islands without paying the charging energy as a penalty, since delocalized states with lower Coulomb energy are avail- able for the transport. Secondly, the islands have to be small enough and the temperature has to be low enough so that the energy required to add a charge carrier to an island exceeds the mean thermal energy of the charge carriers, i.e., E~ ~ k B T. (2) This ensures that the transport of charges is in fact gov- erned by the Coulomb charging energy. With the use of externally applied voltages, the charging energy can then be influenced in order to manipulate the charge carriers. At present, two main types of systems where SCT ef- fects arise are being explored. Much of the work done in the last few years has used lithographically patterned tunnel junction circuits, where metallic islands (mostly made from A1) are separated by oxide layer tunnel barri- ers. In this case, three-dimensional electron gases con- fined to small regions are weakly coupled by the tunnel effect. These systems also allow one to explore charging effects involving Cooper pairs since the metals used to fabricate the circuits are superconductors. At the temper- atures required to satisfy (2), one must apply a magnetic field to keep the metals in the normal state. Specific ex- amples for such circuits are given in the articles by Havi- land et al. [10], Lafarge et al. [11] and Geerligs et al. [12]. Single electron effects also arise when the two-dimen- sional electron gas of a GaAs/A1GaAs heterostructure is confined to small islands by means of Schottky gates. In this case the tunneling resistances of the constrictions separating the islands can be tuned by changing the gate voltages. Further, the islands may be quantum dots with a discrete energy spectrum. Such semiconductor circuits are presented in the articles by Meirav etal. [13], Kouwenhoven et al. [14, 15], and Glattli et al. [16]. A dif- ferent structure where electrons tunnel vertically to the plane of the two-dimensional electron gas is discussed by