Ohm's law in its original form:
The conductivity is constant for a given conductor at a given temperature.(Taken from H.C.Verma).
My Question: When high voltages are impressed across a conductor, valence band starts to overlap with conduction band. On further increasing the voltage, not only the electrons in the conduction band speed up (thereby increasing the current) but also the electrons from the valence band starts conducting (thereby increasing the current). Doesn't this phenomenon violate ohm's law? Because now a small increase in voltage will increase current by a larger factor than with the case when valence band didn't yet overlap with the conduction band.