Quasi-two-dimensional Feynman bipolarons

We study the stability criterion for the formation of two-dimensionally confined large bipolarons. The electrons are treated as bounded within a parabolic potential well while being coupled to one another via the Fr\"ohlich interaction Hamiltonian. Within the framework of the bulk-phonon approximation we adopt the Feynman-polaron model to derive variational results over a wide range of the Coulomb interaction and phonon coupling strengths interpolating between the bulk and the two-dimensional confinement limit. It is shown that the critical values of the electron-phonon coupling constant and the ratio of dielectric constants (η=ε_∞/ε₀) exhibit some nontrivial features as the effective dimensionality is tuned from 3 to 2.