Scaling of 1/f noise in tunable break-junctions

We have studied the $1/f$ voltage noise of gold nanocontacts in electromigrated and mechanically controlled break junctions having resistance values $R$ that can be tuned from $10\text{ }\ensuremath{\Omega}$ (many channels) to $10\text{ }\text{k}\ensuremath{\Omega}$ (single-atom contact). The noise is caused by resistance fluctuations as evidenced by the ${S}_{V}\ensuremath{\propto}{V}^{2}$ dependence of the power-spectral density ${S}_{V}$ on the applied dc voltage $V$. As a function of $R$ the normalized noise ${S}_{V}/{V}^{2}$ shows a pronounced crossover from $\ensuremath{\propto}{R}^{3}$ for low-Ohmic junctions to $\ensuremath{\propto}{R}^{1.5}$ for high-Ohmic ones. The measured powers of 3 and 1.5 are in agreement with $1/f$ noise generated in the bulk and reflect the transition from diffusive to ballistic transport.