Conductance and supercurrent discontinuities in atomic-scale metallic constrictions of variable width

A mechanically controllable break junction is used to study quantum size effects on conduction in metallic constrictions. When changing the constriction radius, we observe reproducible jumps in the conductance which are of the order of 2e^2/h. For contacts adjusted at a jump the conductance switches in time between two values, which we interpret as ``two-level fluctuations'' in the site of a single atom in the constriction. For superconducting point contacts we observe concomitant jumps in the supercurrent of order e/, which is consistent with a recent prediction.