Solving for a bipolaron bound state in strontium titanate (SrTiO₃)

The origin of superconductivity in the doped semiconductor strontium titanate (STO) is not well-understood. Its persistence even at very low carrier densities violates key assumptions of conventional Bardeen-Cooper-Schrieffer (BCS) theory, particularly in that the phonons in this density regime are much faster than the electrons to which they are coupled. The formation of bipolarons, two-electron bound states in a polar medium, serves as a potential electron pairing mechanism beyond the BCS paradigm. Here, the existence of bipolarons in STO is probed using semiclassical analyses and variational calculations to estimate the system’s ground state energy in the weak- and strong-coupling limits of the electron-phonon interaction strength in STO, respectively. It is found that no binding exists in the weak-coupling regime, whereas the strong-coupling regime exhibits strong binding.