Agenda

We develop a theory of superconducting pairing in low-density Strontium titanate due to quadratic coupling of electron density to soft transverse optical phonons. It leads to static attractive potential between electrons which decay length scales inversely with soft optical gap. For low electron densities attraction between electrons is local and transition temperature Tc was found. The Tc(n) dependence in agreement with experimental data for low doping was calculated. Next, we show that suppression of Tc by hydrostatic pressure and strong increase of Tc due to isotopic substitution are explained within our theory.