Quantum Traffic Theory of Single Electron Transport in Nanostructures

Abstract

Consider the possibility of a single electron tunneling through an insulating region between two metallic islands. For this to be possible the electron must somehow acquire a charging energy of the order of e ² /2C, where C is the effective inter-capacitance. At “high temperatures” where T >T _C = e ²/2Ck _B, the charging energy is easily supplied from thermal fluctuations. In the opposite extreme, the so-called Coulomb Blockade regime, T ≪ T _C, the charging energy must be supplied externally for example by applying a voltage across the metal islands; otherwise the tunnelling is blocked. The simplest manifestation of the Coulomb blockade is thus a voltage offset e/2C in the current-voltage characteristics. The most interesting effects however derive from considering the transport of more than one electron through an array of capacitors (Likhaerev, 1988). The transporting/tunnelling electrons become highly correlated in space and time since they must “queue up” to let a definite maximum number of electrons into the capacitor system at a time commensurate with the local charging-energy conditions. The motion is quite subtle because the polarisation field resulting from a propagating electron is distributed over all the metallic islands resulting in electrostatic soliton states forming in the electrode array. It is this solitonic property, a moving particle plus an associated field, which imparts a considerable stability on the electrical properties of a driven capacitor chain at temperatures T ≪ T _c (Barker et al., 1992a). It is not actually necessary for this effect to require tunnelling, any weak “conducting” path such as a charge leakage path, a hopping path or a bottleneck in the conductance map will suffice. It should also be noted that the condition T ≪ T _c must be supplemented by the condition that the series resistance must exceed the quantum resistance R > R ₀ = h/e ² for the effects of quantum fluctuations to be suppressed.