Ohm's law (current proportional to voltage) was first formulated in 1827 and the discoverer George Ohm would be pleased to know that in 2012 the law still holds even at the smallest possible nanoscale. Weber et al. in their report in Science (DOI) do not explain how they would expect conductors to behave in another way at this nanoscale but ventured ahead anyway to create a truly tiny electrical wire, run a current through it and measure resistivity.
A silicon wire 100 nanometers in length, just 4 atoms wide and one atom in height was deposited on silicon by scanning probe lithography (basically patterning the wire one silicon atom at the time). The surface was then doped with phosphine (PH3). The SEM image displayed in the report shows neat rows of silicon dimers topped with PXn molecules and the authors suggest you can distinguish between PH and PH2 molecules. Phosphorus forms P-Si bonds with P atoms on average separated by one nanometer which makes the wire a binary PS compound. The whole surface is then covered in more silicon (molecular beam epitaxy) completing the production process.
Yes, at 4 Kelvin a linear relationship between current and voltage can be reproduced (good news for George) and even a linear relationship between wire length and resistivity. It is curious though that for the construction of the last plot data points are included from an earlier 2007 study (DOI). Nothing wrong with it but that 2007 study also concluded that Ohm's law holds. So how many times can you announce to the world Ohm's Law holds in nanowires?
Weber, B., Mahapatra, S., Ryu, H., Lee, S., Fuhrer, A., Reusch, T., Thompson, D., Lee, W., Klimeck, G., Hollenberg, L., & Simmons, M. (2012). Ohm's Law Survives to the Atomic Scale Science, 335 (6064), 64-67 DOI: 10.1126/science.1214319