Multiorbital superconductivity mediated by transverse optical phonons

Electron-phonon coupling that is responsible for most BCS superconductors typically involves longitudinal phonon mode. For the transverse phonons, typically the electron-phonon coupling vanishes to the first order. This limitation can be overcome for multi-orbital systems, where first order electron-phonon coupling can be induced in the inter-orbital channel. Here on the symmetry grounds, we present some general properties of such TO mode induced multi-orbital superconductivity. We also show that TO mode induced robust superconductivity can be stabilized even in the absence of the spin-orbit coupling, which has been the focus of the previous studies on the TO mode induced superconductivity. Using our theory for the specific case of doped quantum paraelectrics SrTiO₃ and KTaO₃, we highlight the relative role of spin-orbit coupling and multi-orbital physics to explain the aspects of the superconductivity in these materials.