Quantum ferroelectric instabilities in superconducting SrTiO$_3$.
Recent experiments on doped SrTiO$_3$ have shown that superconductivity is favored by its proximity to a quantum ferroelectric instability, suggesting that pairing between its charge carriers could be promoted by quantum criticality. Here, we consider a model that combines a strong coupling theory of superconductors with a standard framework for the soft polar modes in SrTiO$_3$ including their coupling to strain degrees of freedom, lattice dimensionality, displacive nature, and the long-ranged and anisotropic dipolar interactions, which are usually neglected. Our calculations of the superconducting temperature $T_c$ for several applied stresses and cation substitutions reveal that while quantum criticality favors superconductivity,optimal doping is not necessarily pinned to the quantum critical point. We qualitatively reproduce the observed reduction of $T_c$ with hydrostatic pressure and use our model to gain insight into the aforementioned experiments.
Publisher URL: http://arxiv.org/abs/1801.08736
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