Scaling of 1/f noise in tunable break-junctions

We have studied the $1/f$ voltage noise of gold nano-contacts in electromigrated and mechanically controlled break-junctions having resistance values $R$ that can be tuned from 10 $\Omega$ (many channels) to 10 k$\Omega$ (single atom contact). The noise is caused by resistance fluctuations as evidenced by the $S_V\propto V^2$ 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 cross-over from $\propto R^3$ for low-ohmic junctions to $\propto R^{1.5}$ 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.