Low-temperature thermoelectric transport in the disordered two-dimensional electron gas

We study interaction corrections to the thermoelectric transport coefficient $\ensuremath{\alpha}$ and the thermopower $S$ in the two-dimensional disordered electron gas with long-range Coulomb interactions. To this end, we analyze the heat density--density correlation function using the recently derived generalized nonlinear sigma model with particle-hole asymmetry. We present a detailed account of the perturbative calculation of the correlation function, the analysis of its structure, and the derivation of the final results for the transport coefficients. We show that both real and virtual processes give rise to logarithmic interaction corrections to $\ensuremath{\alpha}$ and $S$ with $\ensuremath{\delta}\ensuremath{\alpha}/\ensuremath{\alpha}<0$ and $\ensuremath{\delta}S/S<0$ in the diffusive transport regime $T\ensuremath{\ll}1/\ensuremath{\tau}$, where $T$ is the temperature and $1/\ensuremath{\tau}$ is the disorder scattering rate. A short account of our findings is presented in an accompanying letter.