What would be the nature of solid if there is no energy gap between valence band and conduction band?

The gap between valence band and conduction band shows a minimum energy gap that electrons have to cross in order to be available for conduction of electricity. Now if this gap is eliminated all free electrons will have the minimum energy required to move to the conduction band and for conduction of electricity. Thus the metal or semi-conductor or solid will behave as a superconductor as there is no resistance to electron flow.