铁电涨落介导的自旋-轨道耦合立方系统各向异性超导电性
Anisotropic superconductivity mediated by ferroelectric fluctuations in cubic systems with spin-orbit coupling
摘要：
基于体掺杂SrTiO $_{3}$的超导电性随着接近铁电量子临界点（FE-QCP）而增强的实验观察，我们研究了电子交换低能铁电涨落的立方体系的配对不稳定性.而不是梯度耦合与铁电性相关的晶格畸变，我们认为电子和玻色子铁电场之间的直接耦合，出现在自旋轨道耦合的存在下。工作在弱耦合制度，我们发现，配对相互作用是由软横光学（TO）模式，导致在接近FE-QCP时的$T_{c}$增强。在偶宇称态中，我们发现虽然$s$波态总是获胜，但随着TO模的软化，具有较高库珀对角动量的态成为密切的竞争者。我们表明，立方各向异性的FE波动混合的$s$波和$g$波状态，导致在一个特征的各向异性的间隙函数。当接近FE-QCP时，间隙各向异性表现为非单调的：在降低TO模式频率时，间隙各向异性首先改变符号，然后增加幅度。我们讨论了我们的结果可能的应用到超导态的SrTiO $_{3}$。
英文摘要：
Motivated by the experimental observation that superconductivity in bulk doped SrTiO$_{3}$ is enhanced as a putative ferroelectric quantum critical point (FE-QCP) is approached, we study the pairing instability of a cubic system in which electrons exchange low-energy ferroelectric fluctuations. Instead of the gradient coupling to the lattice distortion associated with ferroelectricity, we consider a direct coupling between the electrons and the bosonic ferroelectric field that appears in the presence of spin-orbit coupling. Working in the weak-coupling regime, we find that the pairing interaction is dominated by the soft transverse optical (TO) mode, resulting in a $T_{c}$ enhancement upon approaching the FE-QCP. Focusing on even-parity states, we find that although the $s$-wave state always wins, states with higher Cooper-pair angular momentum become close competitors as the TO mode softens. We show that the cubic anisotropy of the FE fluctuations mixes the $s$-wave and $g$-wave states, resulting in a characteristic anisotropy of the gap function. The gap anisotropy behaves non-monotonically as the FE-QCP is approached: upon decreasing the TO mode frequency, the gap anisotropy first changes sign and then increases in magnitude. We discuss the possible applications of our results to the superconducting state of SrTiO$_{3}$.
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