Quasiparticle properties of a coupled two-dimensional electron-phonon system

We calculate quasiparticle properties of a weakly polar two-dimensional electron gas by taking into account both electron-electron Coulomb and electron--optical-phonon Fr\"ohlich interactions. Electronic self-energy is calculated exactly in the leading order of the total effective dynamical interaction. The total effective dynamical interaction is obtained within the random-phase approximation (RPA) by starting from the total bare interaction, which includes both Coulomb and Fr\"ohlich interactions and then by screening it with all the bubble diagrams. Our theory thus treats Coulomb and Fr\"ohlich interactions on an equal footing and includes all effects (within the RPA) of Fermi statistics, Landau damping, plasmon-phonon mode coupling, phonon self-energy correction, and dynamical screening. We include finite-thickness effects in actual GaAs-based semiconductor microstructures by considering electron- and phonon- (``slab modes'') confinement effects. Some of our interesting results are (1) Coulomb and Fr\"ohlich interaction effects are nonmultiplicative, and the actual many-body correction for an electron gas is substantially different from the one-polaron result; (2) there are interesting and observable plasmon- and phonon-induced satellite structures in the low-energy side of the electronic spectral function and the density of states; (3) at low electron densities phonons tend to screen Coulomb interaction, whereas at large electron densities electrons screen the Fr\"ohlich interactions; (4) our calculated effective mass and inelastic-scattering length are consistent with the available experimental results.