Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals I: Scattering by phonons, antiferromagnons, and helimagnons

Abstract

We present a technique for an exact solution of the linearized Boltzmann equation for the electrical and thermal transport coefficients in metals in the low-temperature limit. This renders unnecessary an uncontrolled approximation that has been used in all previous solutions of the integral equations for the transport coefficients. Applications include electron-phonon scattering in nonmagnetic metals, as well as the magnon contribution to the electrical and thermal conductivities, and to the thermopower, in metallic ferromagnets, antiferromagnets, and helimagnets. In this paper, the first of a pair, we set up the technique and apply it to the scattering of electrons by phonons, antiferromagnons, and helimagnons. We show that the Bloch $T^5$ law for the electrical resistivity, the $T^2$ law for the thermal resistivity, and the $T$ law for the thermopower due to phonon and antiferromagnon scattering are exact, and determine the prefactors exactly. The corresponding exact results for helimagnons are $T^{5/2}$, $T^{1/2}$, and $T$, respectively. In a second paper we will consider the scattering by ferromagnons.

14pp., 1 fig

References in corpus (4)

• Theory of helimagnons in itinerant quantum systems II: Nonanalytic corrections to Fermi-liquid behavior
• Theory of Helimagnons in Itinerant Quantum Systems III: Quasiparticle Description
• Theory of Helimagnons in Itinerant Quantum Systems IV: Transport in the Weak-Disorder Regime
• Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals II: Scattering by ferromagnons

Cited by in corpus (4)

• Thermal and optical conductivity in the Holstein model at half filling and at finite temperature in the Luttinger-liquid and charge-density-wave regime
• Exact solution of the Boltzmann equation for low-temperature transport coefficients in metals II: Scattering by ferromagnons
• Thermal Transport and Non-Mechanical Forces in Metals
• Method of numerical simulation of interacting quantum gas kinetics on finite momentum lattice