Superconducting dome in ferroelectric-type materials from soft mode instability

We present a minimal theory of superconductivity enhancement in ferroelectric-type materials. Simple expressions for the optical mode responsible soft transition are assumed. A key role is played by anharmonic phonon damping which modulated an external control parameter (electron doping or mechanical strain) causing appearance mode. It shown that superconducting critical temperature $T_{c}$ upon approaching ferroelectric from either side due to Stokes electron-phonon scattering processes promoted strong effects.