We study the thermal conductivity of the disordered two-dimensional electron gas. To this end, we analyze the heat density–heat density correlation function concentrating on the scattering processes induced by the Coulomb interaction in the subtemperature energy range. These scattering processes are at the origin of logarithmic corrections violating the Wiedemann-Franz law. Special care is devoted to the definition of the heat density in the presence of the long-range Coulomb interaction. To clarify the structure of the correlation function, we present details of a perturbative calculation. While the conservation of energy strongly constrains the general form of the heat density–heat density correlation function, the balance of various terms turns out to be rather different from that for the correlation functions of other conserved quantities such as the density-density or spin density–spin density correlation function.

• Received 2 October 2015
• Revised 12 January 2016

DOI:https://doi.org/10.1103/PhysRevB.93.115121