Conductors

In a conductor the valence band and conduction band actually overlap, so there is no gap at all for an electron to cross -- a large population of electrons sits in the conduction band even with zero applied field or at very low temperature, simply because the two bands merge into one continuum. Applying an electric field then only needs to supply enough energy to drift these already-free electrons in a preferred direction to constitute a current; conduction is possible even at low temperatures. Resistivity for a conductor is correspondingly tiny, between $10^{-2}$ a …