Strong Coupling Theory of Superconductivity and Ferroelectric Quantum Criticality in metallic SrTiO$_3$

TL;DR

This paper develops a strong coupling theory linking ferroelectric quantum criticality and superconductivity in doped SrTiO₃, accurately reproducing its phase diagram and elucidating the role of nonlinear couplings.

Contribution

It introduces a comprehensive Eliashberg pairing analysis incorporating nonlinear couplings to explain superconductivity in SrTiO₃ near quantum criticality.

Findings

Quantitative match with experimental phase diagram.

Identification of nonlinear couplings as crucial for phase features.

Estimation of microscopic parameters from data.

Abstract

Superconductivity in doped SrTiO$_3$ has remained an enduring mystery for over 50 years. The material's status as a ``quantum" ferroelectric metal, characterized by a soft polar mode, suggests that quantum criticality could play a pivotal role in the emergence of its superconducting state. We show that the system is amenable to a strong coupling (Eliashberg) pairing analysis, with the dominant coupling to the soft mode being a ``dynamical'' Rashba coupling. We compute the expected $T_c$ for the entire phase diagram, all the way to the quantum critical point and beyond. We demonstrate that the linear coupling is sufficient to obtain a rough approximation of the experimentally measured phase diagram, but that nonlinear coupling terms are crucial in reproducing the finer features in the ordered phase. The primary role of nonlinear terms at the peak of the superconducting dome is to enhance the effective linear coupling induced by the broken order, shifting the dome's maximum into the ordered phase. Our theory quantitatively reproduces the three-dimensional experimental phase diagram in the space of carrier density, distance from the quantum critical point and temperature, and allows us to estimate microscopic parameters from the experimental data.