TEMPERATURE-DEPENDENCE OF THE HARTREE-FOCK APPROXIMATION IN 2 DIMENSIONS

The Hartree-Fock (HF) exchange energy of the two-dimensional electron gas is calculated at nonzero temperatures. The calculation is done self-consistently in that the HF self-energy is included self-consistently in the Fermi-Dirac functions. We also calculate the first and second derivatives of the exchange energy with respect to density, which are useful for density-functional calculations at nonzero temperatures. These calculations may be useful in understanding the temperature dependence of two-dimensional systems such as electrons trapped two dimensionally in semiconductor interfaces.