  he formation of the optical polaron and bipolaron in two-dimensional (2D)
systems are studied in the intermediate electron-phonon coupling regime. The
total energies of 2D polaron and bipolaron are calculated by using the
Buimistrov-Pekar method of canonical transformations and analyzed in the weak,
intermediate and strong coupling regimes. It is shown that the electron-phonon
correlation significantly reduces the total energy of 2D polaron in comparison
with the energy of the strong-coupling (adiabatic) polaron. A charge carrier in
polar crystals remains localized in a 2D potential well when the
electron-phonon coupling constant $\alpha$ is greater than the critical value
$\alpha_{c}\simeq2.94$, which is much lower than a critical value of the
electron-phonon coupling constant $\alpha$ for a 3D system. The critical values
of the electron-phonon coupling constant $\alpha$ and the parameter of Coulomb
repulsion between two carriers $\beta=1/(1-\epsilon_{\infty}/\epsilon_{0})$
(where $\epsilon_{\infty}$ and $\epsilon_{0}$ are the high frequency and static
dielectric constants, respectively), which determine the bipolaron stability
region, are numerically calculated. The obtained results are compared with the
ones obtained by using the Feynman path integral method and the modified
Lee-Low-Pines unitary transformation method.
