Theory of conduction through narrow constrictions in a three-dimensional electron gas

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Abstract
An exact calculation of the quantum conduction through a curvilinear constriction in a three-dimensional electron gas is presented. 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 constrictions formed in atomic-scale point contacts are discussed.