局域耦合到手性势的螺旋狄拉克电流
Helical Dirac Current with Local Coupling to a Chiral Potential
AI总结：
研究圆柱约束下狄拉克本征态携带的螺旋电流纹理，推导手性标量势与狄拉克模式耦合的矩阵元核，揭示自旋选择性耦合的几何选择定则。
摘要：
我们证明，在圆柱约束下，即使在零轨道角动量通道 l = 0 中，精确的狄拉克本征态也携带确定的螺旋守恒电流纹理。对于最低约束模式，狄拉克电流包含非零的方位角分量以及纵向输运，并在两个自旋分辨扇区中表现出相反的手性。该结构也持续存在于倏逝区域。我们进一步推导了静态手性标量势作用于约束 l = 0 狄拉克模式时产生的通道分辨矩阵元核。由此产生的自旋选择性耦合源于狄拉克电流纹理和标量手性势，并产生一个几何选择定则，其中对角通道消失，而非对角转换通道存活。耦合强度由内部采样电流重叠 Jchi(k) 控制，定义为从 0 到 R 的 f(rho) 乘以 jphi_up(rho, k) 乘以 rho d rho 的积分。该量测量手性径向轮廓与自旋向上方位角狄拉克电流密度之间的空间重叠。该机制是完全局域且基于纹理的，无需外部磁场或自旋轨道耦合。在标准狄拉克理论框架内，这项工作确定了自旋选择性响应的最小静态狄拉克几何核，建立了一个基线结构，由此可以系统地发展动态介质、散射和输运形式，以完整描述自旋极化现象，如 CISS。
英文摘要：
We show that a propagating electron wave in the lowest cylindrical channel carries a spin-resolved helical conserved current, and connect this current texture to its local chiral coupling. In a weakly relativistic positive-energy Dirac projection, the two sectors have the same azimuthally symmetric charge density and opposite circulation superposed on longitudinal flow, even though their nonrelativistic orbital harmonic is $l=0$. The current is radially distributed and extends into the evanescent tail. A scalar screw potential couples these modes through a derived vertex expressed by the \emph{chiral current overlap}, $\mathcal J_χ$. Both spatial textures determine the coupling: the environmental radial profile weights the electronic circulation, while the screw harmonic selects correlated changes of spin sector and longitudinal momentum. For a uniform static harmonic, elastic energy conservation makes the first-order spin-flip amplitude vanish within the same transverse mode. Environmental energy exchange is therefore required to activate these selected channels. The same current overlap supplies the spatial kernel for heliciton-assisted inelastic scattering in a companion study and for a subsequent transport treatment of chirality-induced spin selectivity (CISS).
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