Vortices and Charges in Tunnel Junction Networks

Abstract

Films of granular materials have long been modeled as two- (2 D) or three- (3 D) dimensional networks of grains, coupled by tunnel junctions [1]. The electrical resistance of such films is supposed to be concentrated in the junctions, whereas the grains themselves are relatively pure. It has only recently become possible to fabricate such tunnel junction networks artificially, using the lithographic techniques developed for microelectronics. So far only 2D networks have been made. Now parameters can, to a certain extent, be varied independently and theoretical models can be verified quantitatively against experimental results. The networks in ‘natural’ films are irregular, which in the percola-tive limit is an essential aspect. However, many of the important properties are well represented in regular arrays of metallic islands, coupled by identical tunnel junctions. We only consider such arrays here. The interest in tunnel junction arrays is certainly not only prompted by the analogy with the films. The regularity of fabricated tunnel junction arrays also introduces special effects, with their own special physics. In these lectures, we will concentrate on two main topics: the resistive behavior of superconducting arrays and the charging effects associated with the transfer of a single electron or a single Cooper pair. Resistance in 2 D superconductors is usually associated with flow of vortices and, as the title implies, this will play a prominent role here as well. However, in junction arrays we also find a different dissipative regime, better described by coherent phase slip. When vortices are present, they may not move in the familiar viscous way.