Ground-state energy of the polaron gas in two-dimensional semiconductor microstructures

The properties of the ground-state energy of a gas of quasi-two-dimensional interacting polarons are investigated by using the self-consistent theory of Singwi, Tosi, Land, and Sjölander to the response function of the electron system. The electron-phonon contribution to the ground-state energy is calculated for the electron gas confined in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterojunctions and quantum wells with appropriate form factors to take the finite width of the electron layer into account. For the sake of comparison, different approximations (Hubbard, random-phase approximation, and Hartree-Fock) for the screening are also considered.