We describe a variational procedure for calculating the energy of an electron gas in which the long-range Coulomb interaction is truncated by the screening effect of a nearby metallic gate. We use this procedure to compute the quantum capacitance of the system 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.
Categories: cond-mat.mes-hall cond-mat.mtrl-sci