On a two-dimensional electron gas modulated by a periodic potential

After a brief introduction to the semiconductor heterojunction devices in which a two-dimensional electron gas can be realised and can be subjected to a periodic potential through a grating, the linear response function for this periodically modulated system is calculated in the random phase approximation. Two solvable models have been considered, based on the anisotropic electron kinematics arising from the periodic potential. For the first model, approximate and exact results are obtained when (the Fermi level) E F >2t (half the band width) while, for the second model, exact results are obtained when E F >2t as well as E F <2t. Results for the static polarisability and the plasmon dispersion are explicitly displayed.