Temperature-driven narrowing of the insulating gap as a precursor of the insulator-to-metal transition: Implications for the electronic structure of solids

We present a microscopic picture rationalizing the surprisingly steep decrease of the band gap with temperature in insulators, crystalline or otherwise. The gap narrowing largely results from fluctuations of long-wavelength optical phonons---when the latter are present---or their disordered analogs, if the material is amorphous. We elaborate on this notion to show that possibly with the exception of weakly bound solids made of closed-shell atoms, the existence of an insulating gap or pseudo-gap in a periodic solid implies that optical phonons must be present, too. This means that in an insulating solid, the primitive cell must have at least two atoms and/or that a charge density wave is present. As a corollary, a (periodic) elemental solid whose primitive unit contains only one atom will ordinarily be a metal, possibly unless the element belongs to group 18 of the periodic table, consistent with observation. Some implications of the present results for quantum solids are briefly discussed, such as that the ground state of the Wigner crystal must be anti-ferromagnetic. A simple field theory of the metal-insulator transition is constructed that ties long-wavelength optical vibrations with fluctuations of an order parameter for the metal-insulator transition; symmetry-breaking aspects of the latter transition are thereby highlighted.