A perspective on non-local electronic transport in metals: viscous, ballistic, and beyond

Ohm's law for electrical conduction in metals is one of the first concepts taught in any physics curriculum. It is perfectly adequate in almost all practical circumstances, but breaks down in some special, interesting cases. To observe such breakdowns, one requires extremely pure materials, which are rare and often difficult to produce. Excitingly, forefront materials research is leading to the discovery of more and more examples in which one can break the ‘purity barrier’ and explore non-Ohmic transport. The rapid development of the field is seeing equally rapid developments in the understanding of exotic non-Ohmic regimes, but this is not always a smooth progression. New layers of insight often involve reversing what have previously been regarded as established facts. Indeed, the interpretations given of experimental data in many papers published less than a decade ago would (or should!) be different today. The goal of this article is to give an entry-level guide to some of the pertinent issues that have emerged from this intense decade of research, attempting to keep the style of the presentation as informal and non-mathematical as is practical. Although source literature will be cited, no attempt will be made at comprehensive citation, so the paper should not be regarded as a review. Rather, an effort will be made to identify and explain some issues that the authors believe are important but not sufficiently emphasized in the literature to date. In that sense the paper should be regarded as a kind of opinion piece, with, hopefully, some didactic value to a reader with a solid grounding in traditional condensed matter physics.