Conductance quantisation in metallic point contacts

The electrical transport properties of atomic-scale conductors are reviewed, with an emphasis on the relations of this problem with studies on quantum size effects in metallic clusters. A brief introduction is given of the natural formalism for discussing electron transport in ballistic conductors: the Landauer theory. After introducing the experimental techniques, which are used for studying ballistic point contacts in metals, the experimental observations for the conductance of atomic-scale contacts are presented. In order to obtain a full description in terms of the quantum modes for conductance, several recently developed techniques are reviewed, which go beyond straightforward measurement of the conductance. A brief discussion is given of an unusual atomic geometry for gold contacts, which evolve into a chain of freely suspended atoms. Then shell filling effects in sodium nanowires are discussed in the context of the influence of the conductance modes on the total energy of the system. The chapter ends with an outlook on promising new developments.