Isotope effect in superconducting n-doped SrTiO$_3$

Since the discovery of superconductivity in n-doped SrTiO$_3$ half a century ago, this material has played a key role in modern condensed matter physics, in part for its superconducting properties but also its dielectric properties and suitability as a substrate for thin film growth of high-T$_c$ superconductors. We report the influence on the superconducting critical temperature in doped SrTiO$_3$ of the substitution of the natural $^{16}$O atoms by the heavier isotope $^{18}$O. We have found a huge increase of the T$_c$ around $50\%$ and an enhancement by a factor $\sim 2$ of the critical magnetic field H$_{c2}$ for all charge carrier densities. Such a strong impact on T$_c$ and H$_{c2}$, with a sign opposite to conventional superconductors, is unprecedented. Alternative models which take into account the presence of polarons in SrTiO$_3$ or the vicinity of a quantum critical point due to ferroelectric state are now considered and discussed to explain this behavior. Indeed, the unusually large size of the observed isotope effect supports a recent model for superconductivity in these materials based on strong coupling to the ferroelectric soft modes of SrTiO$_3$.