Theory of thermal conductivity in the disordered electron liquid
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ontribution for the JETP special issue in honor of L.V. Keldysh’s 85th birthday
Theory of Thermal Conductivity in the Disordered Electron Liquid1 G. Schwietea and A. M. Finkel’steinb, c, d a Spin
Phenomena Interdisciplinary Center (SPICE) and Institut für Physik, Johannes Gutenberg Universität, Mainz, 55128 Germany b Department of Physics and Astronomy, Texas A&M University, College Station, TX 77843-4242 USA c Department of Condensed Matter Physics, The Weizmann Institute of Science, Rehovot, 76100 Israel d Landau Institute for Theoretical Physics, Moscow, 117940 Russia e-mail: [email protected] Received September 22, 2015
Abstract—We study thermal conductivity in the disordered two-dimensional electron liquid in the presence of long-range Coulomb interactions. We describe a microscopic analysis of the problem using the partition function defined on the Keldysh contour as a starting point. We extend the renormalization group (RG) analysis developed for thermal transport in the disordered Fermi liquid and include scattering processes induced by the long-range Coulomb interaction in the sub-temperature energy range. For the thermal conductivity, unlike for the electrical conductivity, these scattering processes yield a logarithmic correction that may compete with the RG corrections. The interest in this correction arises from the fact that it violates the Wiedemann–Franz law. We checked that the sub-temperature correction to the thermal conductivity is not modified either by the inclusion of Fermi liquid interaction amplitudes or as a result of the RG flow. We therefore expect that the answer obtained for this correction is final. We use the theory to describe thermal transport on the metallic side of the metal–insulator transition in Si MOSFETs. DOI: 10.1134/S1063776116030195
1. INTRODUCTION At temperatures lower than the impurity scattering rate, i.e., in the diffusive regime, the electron liquid acquires various nonanalytic quantum corrections [1, 2]. At low temperatures, the calculation of these corrections requires an RG analysis, which leads to coupled flow equations for the diffusion constant, the interaction constants, and the frequency coefficient [3–7] (for a review, see [2, 8–10]). A systematic procedure for the derivation of the RG equations in disordered electron systems has been developed on the basis of a field-theoretic description [3], the nonlinear sigma model (NLσM). In a series of recent papers [11–13], we extended the NLσM formalism to the study of thermal transport. For this, we introduced time-dependent “gravitational potentials” [14–16] as source fields into the microscopic action. These sources are a convenient tool for generating expressions for the heat density–heat density correlation function from the partition function, which is defined on the Keldysh contour. Knowledge of the correlation function then allows obtaining the thermal conductivity. 1The article is published in the original.
In this paper, we include both the long-range Coulomb interaction and Fermi-liquid-type intera
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