There is no current due to holes in good electrical conductors because they have:

Explanation

When a covalent bond breaks, then the electrons get freed from an atom. This electron moves from the valence band to the conduction band leaving behind a vacancy. This vacancy is called a hole. In case of the conductors, the electrons are loosely bound to the valence band. And they can easily detach from the atoms at the room temperature. So these large numbers of free electrons become available for conduction.An electron moves forward leaving behind a hole. Then another electron captures that hole and moves forward. Thus we can say the hole moves in the opposite direction than the electron and makes up the hole current.In case of conductors, the valence band and the conduction bands overlap. So there are no holes in the conduction band to carry the hole current.Hence there is no hole current in conductors as there is an overlapping of the valence and the conduction bands.