Unconventional scaling of resistivity in two-dimensional Fermi liquids

Abstract

We study the temperature dependence of the electrical resistivity of interacting two-dimensional Fermi liquids. We perform a numerical simulation of the nonequilibrium state based on semiclassical Boltzmann transport theory. A two-dimensional system of quasiparticles on a square lattice serves as a model system. We use a single-orbital tight-binding model of the dispersion. For conceptual purposes, we choose a simple repulsive onsite interaction that leads to quasiparticle scattering and delta-potential scatterers as a model of nonmagnetic impurity scattering. Through our simulation, we demonstrate that deviations from the predictions of standard Fermi-liquid theory can arise due to the nontrivial scattering geometry of umklapp processes, in special cases even in the ultralow-temperature limit. We show through qualitative arguments how these unconventional scaling properties of the electrical resistivity, which are often interpreted as indication of a non-Fermi-liquid state, can arise due to special geometric conditions of the Fermi surface. The appearance of robust deviations from the predictions of Fermi-liquid theory within our simple model presents a viewpoint in order to interpret unconventional transport properties in electron-electron scattering dominated metallic systems.