Triplet pairing due to spin-orbit-assisted electron-phonon coupling.

We propose a microscopic mechanism for spin-dependent attraction in a metal leading to triplet pairing, which is caused by spin-orbit-assisted coupling between electrons and optical phonons in crystals with complex unit cells. Using two examples of crystals with either a cubic or a layered square lattice, we show that spin-orbit-assisted electron-phonon coupling generates triplet pairing with uniquely predetermined tensor structure of the p-wave order parameter.