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arXiv:cond-mat/9703122 · Physical Review Letters

Only Fermi Liquids Are Metals

C. M. Varma

Published Aug 25, 1997• 23 citations
arXivHTMLPDF

Abstract

Any singular deviation from Landau Fermi-liquid theory appears to lead, for an arbitrarily small concentration of impurities coupling to a nonconserved 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.

DOI
10.1103/physrevlett.79.1535

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We consider two-dimensional metals near a Pomeranchuk instability which breaks ${90}^{\ensuremath{\circ}}$ lattice rotation symmetry. Such metals realize strongly coupled non-Fermi liquids with critical fluctuations of an Ising-nematic order. At low temperatures, impurity scattering provides the dominant source of momentum relaxation and, hence, a nonzero electrical resistivity. We use the memory matrix method to compute the resistivity of this non-Fermi liquid to second order in the impurity potential, without assuming the existence of quasiparticles. Impurity scattering in the ddd-wave channel acts as a random ``field'' on the Ising-nematic order. We find contributions to the resistivity with a nearly linear temperature dependence, along with more singular terms; the most singular is the random-field contribution which diverges in the limit of zero temperature.
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