Ohm's law deviation

In terms of superconductivities and diodes (I do not know anything else except these), Ohm's law deviate from a linear relation. I search many titles or tags for this but I did not understand properly how it becomes. I wonder somethings related with this.

• What is the basic of this deviation?

• How it is deviate?

• Why there is linear relation for metal conductors, if is it true?

• Many physics things are linear under certain approximations and limits. Some things aren't. Explaining why semiconductors may (or may not) obey Ohm's "Law" takes a good intro to semiconductor physics. Note that capacitors and inductors don't obey Ohm's law either, and they aren't even weird materials. Apr 5 '16 at 14:11

Ohm's law is a misnomer. It is not actually a true law, in the sense of Coulomb's of Ampère's; rather it is a 'rule of thumb' that applies pretty well in most circumstances. You will certainly not get a nobel price for finding an exception! A more general form of Ohm's law is $$\mathbf{J} = \sigma \mathbf{E},$$where $\mathbf{J}$ is the current density, $\sigma$ the conductivity and $\mathbf{E}$ the electric field. Now in this form, you can easily find a classical derivation, due to Drude, (which is totally inaccurate but does make some good qualitative predictions