Simple variational method for calculating energy and quantum capacitance of an electron gas with screened interactions

We describe a variational procedure for calculating the energy of an electron gas in which the long-range Coulomb interaction is truncated, for example by the screening effect of a nearby metallic gate. We use this procedure to compute the quantum capacitance of a two-dimensional electron gas next to a metallic gate as a function of electron density and spin polarization. The accuracy of the method is verified against published Monte Carlo data. The results compare favorably with a recent experiment.