Question

Do all metal show the expected Hall effect? If not what is the reason?

Answer 1

In the metal, the charge carriers are conduction electrons, so we expect a negative value of the Hall coefficient.

In a metal, the highest energy band is only partially full. Thus, it is easy to raise electrons to a higher energy state with an electric field, and a metal is a good conductor. Also, the number of available electrons for conduction is just the number of electrons in the highest energy band. This number is independent of temperature, so one expects that the conduction electron carrier density (and therefore the Hall coefficient) will be independent of temperature.

At a certain point you will see the Hall coefficient change sign, indicating the change from the conductivity being dominated by the donated holes to being dominated by the intrinsic conduction electrons that are thermally excited across the bandgap. Hence we conclude that all metals need not show the expected Hall effect.