标题： 强耦合超导理论与金属SrTiO$_3$中铁电量子临界性 显示英文标题

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

摘要： 掺杂SrTiO$_3$中的超导性在过去50多年里一直是一个持久的谜团。 这种材料作为“量子”铁电金属的状态，其特征是存在一个软极化模式，这表明量子临界性可能在其超导态的出现中起着关键作用。 我们表明，该系统适合进行强耦合（Eliashberg）配对分析，其中与软模式的主要耦合是一种“动态”的Rashba耦合。 我们计算了整个相图中的预期$T_c$，一直到量子临界点甚至更远。 我们证明线性耦合足以获得实验测量相图的粗略近似，但非线性耦合项在再现有序相中的细节特征中是至关重要的。 在超导穹顶峰值处，非线性项的主要作用是增强由破缺序引起的有效线性耦合，将穹顶的最大值转移到有序相中。 我们的理论在载流子密度、距离量子临界点的距离和温度的空间中定量地再现了三维实验相图，并使我们能够从实验数据中估计微观参数。 显示英文摘要

摘要： 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.