The two-phonon pairing mechanism in SrTiO3 gives a small, monotonically doping-dependent Tc because the attraction is controlled by high-energy phonons, not the soft mode.
Instead, for the quadratic model, it scales as 1 /ω3
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Two-phonon pairing and superconductivity in $SrTiO_3$
The two-phonon pairing mechanism in SrTiO3 gives a small, monotonically doping-dependent Tc because the attraction is controlled by high-energy phonons, not the soft mode.