We study the thermoelectric effect of two-dimensional metals on a square lattice within semiclassical Boltzmann transport theory with particular focus on electron-electron scattering. We compute the electrical conductivity and the Seebeck coefficient as a function of band filling and temperature for generically chosen hopping parameters in a two-dimensional tight binding model. The Boltzmann equation is solved numerically after computing the full collision integral taking the angular and radial degrees of freedom into account. These degrees of freedom of the collision integral, neglected in the standard single-relaxation-time approximation, play an important role if the transport coefficients show unconventional features. Within our detailed numerical simulation, we show that the widely used Mott formula to compute the Seebeck effect is not sufficient to describe the thermoelectric effect in the presence of strong electron-electron scattering. Furthermore, we study the Seebeck coefficient and its temperature dependence in the vicinity of a Lifshitz transition and demonstrate that it shows remarkable parallels to transport features near a quantum critical point. This paper is published as "Phys. Rev. B 88, 115128 (2013)"http://link.aps.org

We study the temperature dependence of the electrical resistivity of interacting two-dimensional metallic systems. We perform a numerical simulation of the nonequilibrium state based on semiclassical Boltzmann transport theory. Through our simulation, we demonstrate that deviations from the predictions of standard Fermi-liquid theory can arise due to the special scattering geometry of umklapp processes, in special cases even in the ultra-low-temperature limit. Umklapp scattering is required to relax the total momentum of the quasiparticle distribution function. We investigate the transport properties of a two-dimensional system of quasiparticles with repulsive on-site interactions and nonmagnetic impurity scattering on a square lattice with a single-orbital tight-binding model of the dispersion. We demonstrate that 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 novel viewpoint in order to interpret unconventional transport properties in electron-electron scattering dominated metallic systems.Comment: 11 pages, 9 figure

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The in-plane resistivity of the high-temperature oxide superconductor La2−xSrxCuO4 [LSCO] shows a strong growth of a contribution linear in temperature as the doping is reduced in the overdoped region toward optimal. This linear term is a signature of non-Fermi liquid behavior. We find that the appearance of a linear term in the resistivity can arise in a semiclassical Boltzmann transport theory which uses renormalized quasiparticle scattering rates derived in a functional renormalization group calculation and an empirical band structure fitted to angle-resolved photoemission spectroscopy data on LSCO. The linearized Boltzmann equation is solved numerically by discretizing the Brillouin zone in a way that fits best to the Fermi surface geometry. The main trends in the development of the anomalous temperature dependence are well reproduced. There is a substantial underestimation of the magnitude of the resistivity which is expected in view of the moderate to weak values we chose for the onsite repulsion to stay within the one-loop renormalization group approximation. The analysis was extended to the Seebeck coefficient with similar agreement with the main trends in the data.This article is accepted for publication (Jan. 2nd, 2013): Phys. Rev. B 87, 035129 (2013 http://link.aps.org/

Recent experiments revealed non-Fermi-liquid resistivity in the unconventional superconductor Sr 2 RuO 4 when strain pushes one of the Fermi surfaces close to a van Hove singularity. The origin of this behavior and whether it can be understood from a picture of well defined quasiparticles is unclear. We employ a Boltzmann transport analysis beyond the single relaxation-time approximation based on a single band which undergoes a Lifshitz transition, where the Fermi surface crosses a van Hove singularity, either due to uni-axial or epitaxial strain. First analytically investigating impurity scattering, we clarify the role of the diverging density of states together with the locally flat band at the point of the Lifshitz transition. Additionally including electron-electron scattering numerically, we find good qualitative agreement with resistivity measurements on uni-axially strained Sr 2 RuO 4 , including the temperature scaling and the temperature dependence of the resistivity peak. Our results imply that even close to the Lifshitz transition, a description starting from well-defined quasiparticles holds. To test the validity of Boltzmann transport theory near a van Hove singularity, we provide further experimentally accessible parameters, such as thermal transport, the Seebeck coefficient, and Hall resistivity and compare different strain scenarios.