The concept of ferroelectricity is now often extended to include continuous inversion symmetry-breaking transitions in various metals and doped semiconductors. Paraelectric metals near ferroelectric quantum criticality, which we term ‘quantum paraelectric metals,’ possess soft transverse optical phonons which can have Rashba-type coupling to itinerant electrons in the presence of spin-orbit coupling. We find through the Kubo formula calculation that such Rashba electron-phonon coupling has a profound impact on electron spin transport. While the spin Hall effect arising from non-trivial electronic band structures has been studied extensively, we find here the presence of the Rashba electron-phonon coupling can give rise to spin current, including spin Hall current, in response to an inhomogeneous electric field even with a completely trivial band structure. Furthermore, this spin conductivity displays unconventional characteristics, such as quadrupolar symmetry associated with the wave vector of the electric field and a thermal activation behavior characterized by scaling laws dependent on the phonon frequency to temperature ratio. These findings shed light on exotic electronic transport phenomena originating from ferroelectric quantum criticality, highlighting the intricate interplay of charge and spin degrees of freedom.

铁电性的概念现在经常扩展到包括各种金属和掺杂半导体中的连续反演对称破缺跃迁。接近铁电量子临界点的顺电金属，我们称之为“量子顺电金属”，拥有软横向光学声子，在存在自旋轨道耦合的情况下，可以与流动电子进行拉什巴型耦合。通过Kubo公式计算我们发现，这种Rashba电子声子耦合对电子自旋输运有着深远的影响。虽然对非平凡电子能带结构产生的自旋霍尔效应已进行了广泛研究，但我们发现 Rashba 电子声子耦合的存在可以产生自旋电流，包括自旋霍尔电流，以响应不均匀的电场，甚至具有完全平凡的能带结构。此外，这种自旋电导率显示出非常规的特征，例如与电场波矢量相关的四极对称性以及以取决于声子频率与温度比的比例定律为特征的热激活行为。这些发现揭示了源自铁电量子临界性的奇异电子传输现象，强调了电荷和自旋自由度的复杂相互作用。