Theory of superconductivity due to Ngai's mechanism in lightly doped SrTiO3

Abstract

We develop a theory of superconducting pairing in low-density strontium titanate due to the quadratic coupling of electron density to soft transverse optical phonons first proposed by Ngai [Phys. Rev. Lett. 32, 215 (1974)]. This leads to a static attractive potential between electrons with decay length ${l}_{\mathrm{eff}}$ that scales inversely with soft optical gap ${\ensuremath{\omega}}_{T}$. For low electron densities $n\ensuremath{\le}{10}^{18}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, attraction between electrons is static and local in space; thus the transition temperature ${T}_{c}$ was found using known results for low-density electron gas. The ${T}_{c}(n)$ dependence for low doping was calculated and found to be in agreement with experimental data. In addition, we show that suppression of ${T}_{c}$ by hydrostatic pressure and strong increase in ${T}_{c}$ due to isotope substitution $^{16}\mathrm{O}{\ensuremath{\rightarrow}}^{18}\mathrm{O}$ observed experimentally also can be explained within our theory.