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

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), 10.1103/PhysRevLett.32.215]. This leads to a static attractive potential between electrons with decay length l_eff that scales inversely with soft optical gap ω_T. For low electron densities n ≤10¹⁸ cm⁻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 ¹⁶O→¹⁸O observed experimentally also can be explained within our theory.