Analysis of Fr\"ohlich bipolarons

Following a resurgence of interest in dilute superconductivity in polar semiconductors, we perform a variational calculation to probe the existence of Fr{\"o}hlich bipolarons in these materials. Our solution is capable of interpolating between the weak- and strong-coupling limits of the electron-phonon interaction. We predict bipolaron formation in solely the strong-coupling regime, and we are not aware of any existing materials at these parameter values. However, imposing an extrinsic electron size constraint to mimic confinement on the sub-micron scale produces binding in new parts of the phase diagram, including at weak coupling, within reach of the near-ferroelectric perovskites.