Analysis of Fröhlich bipolarons

Following a resurgence of interest in dilute superconductivity in polar semiconductors such as strontium titanate (STO) and potassium tantalate (KTO), we perform a variational calculation to probe the existence of Fröhlich bipolarons in this class of materials. Our solution is capable of interpolating between the weak- and strong-coupling limits of the electron-phonon interaction strength. We predict bipolaron formation in the strong-coupling regime, and binding at weak-coupling (close to ferroelectricity) only when the electron size is extrinsically restricted. We find measurable binding at STO parameters that may be relevant to experiment, and are not aware of any materials in the strong-coupling regime.