发表机构
Graduate School of Science, Hokkaido University（北海道大学理学研究科）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究构建了周期晶体中热力学电环偶极子的体有序参数，建立其与绝缘体系本征纵向自旋电导率的关联，通过Kane--Mele模型验证了铁轴序的输运表现。
AI 中文摘要
电环偶极子（ETD）表征铁轴序，但周期晶体中其体定义一直难以明确，因为常规多极算子涉及定义模糊的位置算子。本文通过将空间变化电场与相对论自旋诱导的电极化耦合，构建热力学电环偶极子，所得表达式具有规范不变性，可为铁轴相提供体有序参数。进一步建立电环偶极子的化学势导数与绝缘体系中本征纵向自旋电导率的直接关联。为验证该构建，构造Kane--Mele模型的最小铁轴扩展，电环偶极子仅在铁轴相中有限，且在小带隙附近显著增强，伴随可观的纵向自旋电流。研究确立了晶体固体中电环偶极子的热力学理论，并将纵向自旋电导率识别为铁轴序的直接输运表现。
英文摘要
Electric toroidal dipoles (ETDs) characterize ferroaxial order, yet their bulk definition in periodic crystals has remained elusive because conventional multipole operators involve the ill-defined position operator. Here we formulate a thermodynamic ETD by coupling a spatially varying electric field to the relativistic spin-induced electric polarization. The resulting expression is gauge invariant and provides a bulk order parameter for ferroaxial phases. We further establish a direct relation between the chemical-potential derivative of the ETD and the intrinsic longitudinal spin conductivity in insulating systems. To demonstrate the formulation, we construct a minimal ferroaxial extension of the Kane--Mele model. The ETD becomes finite exclusively in the ferroaxial phase and is strongly enhanced near a small band gap, accompanied by a sizable longitudinal spin current. Our results establish a thermodynamic theory of ETDs in crystalline solids and identify the longitudinal spin conductivity as a direct transport manifestation of ferroaxial order.
Comments9 pages, 5 figures
