Quantum Ferroelectric Instabilities in Superconducting SrTiO3

Abstract

We examine the effects of strain and cation substitution on the superconducting phase of polar semiconductors near a ferroelectric quantum phase transition with a model that combines a strong coupling theory of superconductors with a standard microscopic framework for displacive polar modes coupled to strain degrees of freedom. Our calculations reveal that the superconducting transition temperature Tc is enhanced by proximity to the ferroelectric instability from the disordered side, while it is generally suppressed in the ordered phase due to its increase in dielectric stiffness and a reduction of critical fluctuations from dipolar induced anisotropies. The condensation of the pairing phonon excitations generates a kink in Tc at a charge density that is generally lower than that of the quantum critical point (QCP) and where both superconducting and ferroelectric orders set in. We apply our model to SrTiO_3 and find that the antiadiabatic limit places the kink nearly at its QCP. As the QCP is pushed to higher charge densities with either tuning parameter, we find that the dome narrows and sharpens. Our model is in qualitative and fair quantitative agreement with the recent observation of overlapping ferroelectric-like and superconducting instabilities in n-doped Sr_(1-x)Ca_xTiO_3 and strain tuning of Tc in n-doped SrTiO_3. We compare our results to previous models invoking order-disorder lattice dynamics to describe the pairing excitations.