Strontium titanate is a room temperature cubic perovskite with many features including quantum paraelectricity where quantum fluctuations are large enough to prevent ferroelectric order from forming (incipient ferroelectricity). A lowering of crystal symmetry occurs at ~105 K and, in Nb doped or oxygen depleted samples, superconductivity can occur with critical temperatures up to about 0.4 K at optimal doping; the superconducting dome is reminiscent of those seen in high- superconductors where the systems are close to magnetic quantum critical points. One possibility is that the pairing mechanism is from ferroelectric phonons and that tuning towards or away from the ferroelectric phase transition therefore affects .

Using Eliashberg strong coupling theory and assuming coupling only to one ferroelectric phonon mode, we have explored both oxygen isotope substitution (upper plot) and strain (lower plot) as means of tuning towards ferroelectricity. We predict large increases in , of 50% or more; with experimental work in qualitative agreement. Much work is yet do be done to form an accurate description for superconductivity in strontium titanate due to the low carrier densities and unknown symmetry of the superconducting order parameter.

**Key papers:**

- Quantum Critical Origin of the Superconducting Dome in SrTiO
_{3}

Jonathan M. Edge, Yaron Kedem, Ulrich Aschauer, Nicola A. Spaldin, and Alexander V. Balatsky

Phys. Rev. Lett. 115, 247002 (2015)

arXiv:1507.08275 - Superconductivity at low density near a ferroelectric quantum critical point: doped SrTiO
_{3}

Peter Wölfle, Alexander V. Balatsky

Phys. Rev. B 98, 104505 (2018)

arXiv:1803.06993 - Strain and ferroelectric soft-mode induced superconductivity in strontium titanate

K. Dunnett, Awadhesh Narayan, N. A. Spaldin, and A. V. Balatsky

Phys. Rev. B 97, 144506 (2018)

arXiv:1712.08368