In our social life, law-breaking is penalized. Violation of well-established physical laws—if demonstrated by sound experimental evidences or founded upon rigorous theoretical predictions—usually causes excitement as a harbinger of new physics. In this experimental paper, we report evidences of violation of one of the basic laws that govern electrical circuits, Ohm’s law, in nanoscale charge-transport networks formed at the interface between two oxides, ${\mathrm{LaAlO}}_3$ and ${\mathrm{SrTiO}}_3$.

This particular two-dimensional interface system has attracted intense interest from condensed matter physicists, because it displays a rich range of properties, not least, superconductivity and magnetism. It is then fundamentally interesting to ask the following question: Will we see new physics if the interface is shrunk into very narrow nanowires or a network of such nanowires? Using a sharp conductive probe like an “Etch-a-Sketch” toy to induce or erase conducting nanowires at the ${\mathrm{LaAlO}}_3/{\mathrm{SrTiO}}_3$ interface, we have created a number of nanoscale networks for charge transport and investigated how current and voltage are related to each other in such networks. Our findings are quite extraordinary: Ohm’s law is violated in two different respects. First, while Ohm’s law states that the resistance of a wire should be proportional to its length, we have observed instead a length-independent resistance, whose value is of the order of the resistance quantum $h/e^2$. Second, while a voltage is only established along the path of a current according to Ohm’s law, we have observed “nonlocal” resistances—voltages that are separated from current paths by as much as 10 micrometers.

Precisely what microscopic mechanisms are operating behind these fascinating findings is not yet well understood. But we hope that the findings will be the kindling and match that are needed to ignite a fire.