Only Fermi-Liquids are Metals

Abstract

Any singular deviation from Landau Fermi-liquid theory appears to lead, for arbitrarily small concentration of impurities coupling to a non-conserved quantity, to a vanishing density of states at the chemical potential and infinite resistivity as temperature approaches zero. Applications to copper-oxide metals including the temperature dependence of the anisotropy in resistivity, and to other cases of non Fermi-liquids are discussed.