Effect of dynamical screening on the polaron cyclotron-resonance mass of a two-dimensional electron gas in GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures

The cyclotron-resonance mass of a two-dimensional electron gas interacting with bulk LO phonons is investigated as a function of the magnetic field strength and of the electron density. A theory is presented and worked out numerically, for the first time, which includes a full dynamical screening of the electron-phonon interaction for arbitrary magnetic field strength. It is found that near the magnetophonon resonance a dynamical screening theory and a static screening theory give, within 1%, the same contribution to the polaron cyclotron-resonance mass renormalization in the region of experimentally relevant electron densities for a GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructure.