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A dielectric instability of a collection of charged fermions interacting via Coulomb forces and subjected to a random external field is pointed out. It is shown that, as a result of localization produced by the random potential, an RPA Coulomb field can generate a dielectric instability, both static or frequency dependent, resulting in a static or oscillating crystalline arrangement of the fermions. In simple metals, such as the alkali metals, this mechanism is shown to provide an explanation of the existence of the crystal lattice and of acoustic phonons.

A Dielectric Instability of a Fermion Gas in a Random Potential