Acoustical polarons and bipolarons in two dimensions

Using the Feynman path-integral formalism we study the ground state of the acoustical polaron and bipolaron in two dimensions. The phase diagram for the self-trapping of polarons is obtained. For a Debye cutoff of k(0)<130 the self-trapping transition is continuous while for k(0)>130 it is discontinuous and the polaron mass exhibits a discontinuity as function of the electron-phonon coupling constant (alpha). A phase diagram for the polaron-bipolaron transition is obtained and we found that (1) the bipolaron transition is a first-order transition and (2) it is also possible between two polarons which are in the quasifree state, i.e., not self-trapped. At the transition point the effective mass changes substantially. Analytic results for the energy and the phase diagram in the weak- and strong-coupling constant regime are also obtained.