Theory of Conduction through Quantum Necks

Abstract

The conductance of a narrow ballistic neck connecting two three-dimensional electron gas is calculated exactly for different neck geometries. We show that the conductance behavior presents significant differences with respect to the two-dimensional case. Importantly, we find that the conductance of a circular point contact deviates from the classical Sharvin result and the conductance per unit area is not constant except in the limit of macroscopic areas. We show that quantum finite size effects can be taken into account by a simple semiclassical correction to the Sharvin formula. Recent experiments and calculations on quantum necks formed in atomic-scale point contacts are discussed.