Abstract
We consider two-dimensional metals near a Pomeranchuk instability which breaks 90$^\circ$ 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 non-zero 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 $d$-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.
Highlights
A large number of recent experiments have provided evidence of Ising-nematic correlations in quasi-two-dimensional metals
Ising nematic order corresponds to a spontaneous breaking of the 90◦ rotational symmetry of the square lattice
We find that the random field disorder is especially effective in relaxing the total momentum: in perturbation theory in the strength of the random-field, we obtain a resistivity which diverges as T → 0
Summary
A large number of recent experiments have provided evidence of Ising-nematic correlations in quasi-two-dimensional metals. A similar belief applies to the resistivity of fermions coupled to a transverse gauge field,[43,44] a system with a low energy theory closely related[36] to that of the Ising-nematic quantum critical point These arguments ignore constraints arising from the relaxation of the total momentum of the system,[45,46] as momentum can only be degraded by impurities or via umklapp scattering. The holographic duals[66,67,68,69,70,71] do not include Fermi-surface contributions, and exclusively consider the analog of the dynamics of the bosonic order parameter scattering off random field-like perturbations The dominance of the latter bosonic processes over the Fermi surface terms in our present analysis lends support to the holographic program for non-Fermi liquid transport.
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