Fr"ohlich Bipolarons in Two-Dimensional Materials

Motivated by the progress in the physics of two-dimensional materials and the recent two-dimensional generalization of the Fröhlich model, we study the formation of bipolarons in polar monolayers. Because of very special nonlocal dielectric screening in two dimensions, this setting differs qualitatively from the conventional Fröhlich model. In monolayers, (i) long wavelength LO phonons acquire a nontrivial dispersion; (ii) the Fröhlich electron-phonon vertex becomes momentum-dependent and regular at small momenta; and (iii) direct repulsion between charge carriers takes the Keldysh-Rytova form. Using the Feynman path-integral variational approach, we show that the region in the parameter space where stable bipolarons exist is strongly modified compared to the usual quasi-two-dimensional model with dispersionless phonons. Specifically, in the most favorable limit, when the ratio σ 0 of the static polarizability to the high-frequency polarizability tends to infinity, the lower critical coupling, sufficient for the formation of bipolarons, can be made arbitrarily small. More surprisingly, we demonstrate that no stable bipolarons can exist in the strong coupling limit: in the isolated monolayer the stability region is always confined to a finite range of coupling constants. In general, the stability region is strongly shifted toward large values of the polarizability ratio σ 0, well beyond the parameter regimes in representative crystals, which indicates that polar monolayers do not favor bipolarons.