It is shown that in two-dimensional semiconductors, the electron-phonon interaction and polaron
mass correction are both significantly enhanced by the Rashba spin-orbit coupling. The mass
correction is positive for the upper Rashba branch and negative for the lower Rashba branch. Both
Rashba branches have the same polaron binding energy, which is higher than that for systems in the
absence of spin-orbit interaction. To the leading order, the correction to the binding energy is
proportional to the square of the spin-orbit coupling strength.