Two-dimensional electron gas at finite temperature

Abstract

The internal energy of a two-dimensional electron fluid was evaluated explicitly for low but finite temperature as a function of ${r}_{s}$, taking into consideration the first- and second-order exchange and ring diagrams. It is found that the energy varies almost quadratically with temperature but involves logarithmic terms, one of them being exactly the square of another. From the temperature-dependent energy, the specific-heat effective mass ${m}^{*}$ was determined. In an approximation $\frac{{m}^{*}}{m}=1+0.168{n}^{\ensuremath{-}\frac{1}{2}}\ifmmode\times\else\texttimes\fi{}{10}^{6}$, where $n$ is the density.