Exact calculations of the differential ballistic conductance of small contacts both in two- and three-dimensional electron gases are presented. As the voltage increases, the initial quantized values of the conductance evolves into higher or lower noninteger multiples of ${2\mathrm{e}}^2$/h. For abrupt constrictions, nonadiabatic effects manifest themselves as an overall decrease of the conductance toward saturation at very high voltages. This behavior is consistent with recent experiments in two-dimensional point contacts. Importantly, we find that the conductance-voltage characteristics in three-dimensional systems depends on the degeneracy of transversal modes. The possibility of observing nonlinear effects in actual experiments on atomic-scale metallic contacts is discussed.

• Received 18 February 1997

DOI:https://doi.org/10.1103/PhysRevB.55.R16029