Phonon-mediated electron attraction in SrTiO${}_3$ via the generalized Fröhlich and deformation potential mechanisms

Abstract

Superconductivity in doped SrTiO${}_3$ was discovered in 1964, the first superconducting transition observed in a doped semiconductor. However, the mechanism of electron pairing in SrTiO${}_3$ remains a subject of debate. By developing a theoretical framework to incorporate dynamical lattice screening in the electronic Coulomb interactions of semiconductors and insulators, we demonstrate analytically that linear long-range coupling of electrons to multiple longitudinal optical phonons, described by a generalized Fröhlich mechanism, can result in superconductivity in SrTiO${}_3$. Moreover, by combining our theory with first-principles calculations, we reveal an additional attractive interaction between electrons in SrTiO${}_3$ due to the deformation potential mechanism, arising from the mixed ionic-covalent character of the Ti-O bond. Our results may have implications for the emergence of phonon-mediated electron attraction and superconductivity in a broad range of materials.