Possible mechanism for superconductivity in doped SrTiO_{3} - D. van der Marel; F. Barantani; C. W. Rischau (Physical Review Research, 2019)
The soft ferroelectric phonon in SrTiO_{3} observed with optical spectroscopy has an extraordinarily strong spectral weight which is much stronger than expected in the limit of a perfectly ionic compound. This “charged phonon” effect in SrTiO_{3} is caused by the close-to-covalent character of the Ti-O ionic bond and implies a strong coupling between the soft ferroelectric phonon and the interband transitions across the 3-eV gap of SrTiO_{3}. We demonstrate that this coupling leads, in addition to the charged phonon effect, to a pairing interaction involving the exchange of two transverse optical phonons. This process owes its relevance to the strong electron-phonon coupling and to the fact that the interaction mediated by a single transverse optical phonon vanishes at low electron density. We use the experimental soft phonon spectral weight to calculate the strength of the biphonon mediated pairing interaction in the electron-doped material and show that it is of the correct magnitude when compared to the experimental value of the superconducting critical temperature. Biphonon exchange is therefore an important pairing mechanism at low doping, and may be the key to understanding the occurrence of superconductivity in doped SrTiO_{3} and other low electron density materials.