Charging Effects in Mesoscopic Tunnel Junctions

It is now possible to fabricate extremely small tunnel junctions with a capacitance C < 10^ {-15}F. In such a case the charging energy e^2/2C can be larger than the thermal energy kT, and many novel effects are possible. We examine the theory of single tunnel junctions in the semiclassical and coherent limits, and determine the effect of the charging energy on junction dynamics in the two models. The predicted experimental signature of the two approaches, including I-V characteristics, hysterisis, effect of an alternating current, noise and power spectra, are discussed in detail. Understanding of the coherent model requires a detailed understanding of the dynamics of Zener tunnelling. We define a new quantity, the Zener time, which describes the time for a Zener transition, and calculate it in the sudden and adiabatic limits. We also derive expressions for the Zener tunnelling probability at finite times. We then look at two junction connected in series and driven by a voltage source in the semiclassical model. Using stochastic simulations and a master equation approach we show how such a system can have a staircase I-V characteristics. Relevant experiments are reviewed. We go on to show how this may be related to tunneling measurements on granular high T _{rm c} superconductors. We discuss possible device applications, such as transistors and switches. We conclude with an "effective equation" approach for the semiclassical model, which gives the approximate dynamics of the stochastic process. This approach is then extended to a chain of junctions, and is used to demonstrate the possibility of a new collective excitation, the charge effect soliton. We discuss the soliton solution in detail, and consider its experimental consequences.