I was rereading Purcell's Electricity and Magnetism as research for another question, and I found this passage:
In metals Ohm's law is obeyed exceedingly accurately up to current densities far higher than any that can be long maintained. No deviation has ever been clearly demonstrated experimentally. (Second edition, 1985, section 4.5, p143.)
Here all characteristics of the metal, including temperature, must be kept constant, and in such conditions Purcell states that no deviation from a linear relation between electric field and current density has been demonstrated.
Now, this book is relatively outdated (two pages back it touches briefly on superconductivity and mentions that the highest Tc on record is 21 K), so I wonder whether the fact above, admittedly less technologically crucial than high-Tc superconductivity, is still held to be experimentally true, or whether deviations from linearity have in fact been observed. Purcell goes on to state that
According to one theoretical prediction, departures on the order of 1 percent might be expected at a current density of 10$^9$ amps/cm$^2$
though I'm having some trouble guessing whether we have technology to reach such current densities.
To put things on a more concrete footing, then: have deviations from Ohm's law in metals been observed? Is this an active question in any field of research? Do confirmations of this follow from other, related research? Or, alternatively: has the prediction above been verified or falsified? Do we have technology to test those regimes? (if not, what ranges are experimentally viable?) Additionally, can someone supply a reference to the theoretical prediction?
Brief edit: I just got my hands on a sample of the new (2013) edition of Purcell (now in SI units!), revised by Morin. They have updated the superconductivity bit to include high-Tc SCs, but the Ohm's law passage remains much the same. They do mention that the current density above is
over a million times stronger than normal, but don't specify what the state of the art is in current density, and don't give references to the 'theoretical prediction'. It's real nice to have that book brought back to SI life, though!