Invited
Superconductivity and quantum criticality in doped ferroelectrics

Quantum phase transitions may be reached in many ferroelectric systems by supressing the Curie temperature to absolute zero using a quantum tuning parameter such as chemical substitution or hydrostatic pressure. We present experimental and model results revealing the nature of the quantum critical regime which persists over wide ranges in temperature and tuning parameter and includes a low temperature quantum polar-elastic phase. The occurrence of superconductivity in electron-doped SrTiO3 and related materials at low carrier densities points to the presence of an unusually strong pairing interaction that has puzzled scientists for several decades. We discuss new experiments on the pressure dependence of the superconducting transition temperature, Tc, that sheds light on the nature of this interaction. We find that Tc increases dramatically when the energy gap of ferroelectric critical modes is suppressed, i.e., as the ferroelectric quantum critical point is approached, in a way reminiscent of behaviour observed in magnetic counterparts. However, in contrast to the latter, the coupling of itinerant electrons to the critical modes in ferroelectrics is predicted to be small. We present a superconductivity model to make quantitative comparisons with experiments and show that an enhancement of Tc near to a ferroelectric quantum critical point arises due to the virtual exchange of longitudinal hybrid-polar-modes, even in the absence of a direct coupling to the transverse critical modes.