We report a new type of spin-orbit coupling (SOC) called geometric SOC. Starting from the relativistic theory in curved space, we derive an effective nonrelativistic Hamiltonian in a generic curve embedded into flat three dimensions. The geometric SOC is $O(m^{-1})$, in which $m$ is the electron mass, and hence much larger than the conventional SOC of $O(m^{-2})$. The energy scale is estimated to be a hundred meV for a nanoscale helix. We calculate the current-induced spin polarization in a coupled-helix model as a representative of the chirality-induced spin selectivity. We find that it depends on the chirality of the helix and is of the order of $0.01 \hbar$ per ${\rm nm}$ when a charge current of $1~{\rm \mu A}$ is applied.

中文翻译：

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几何自旋轨道耦合和手性诱导的自旋选择性

我们报告了一种称为几何 SOC 的新型自旋轨道耦合 (SOC)。从弯曲空间中的相对论理论出发，我们在嵌入平面三维的一般曲线中推导出一个有效的非相对论哈密顿量。几何SOC是$O(m^{-1})$，其中$m$是电子质量，因此比$O(m^{-2})$的传统SOC大得多。纳米级螺旋的能级估计为一百 meV。我们在耦合螺旋模型中计算电流诱导的自旋极化，作为手性诱导的自旋选择性的代表。我们发现它取决于螺旋的手性，当施加 $1~{\rm \mu A}$ 的充电电流时，它的数量级为 $0.01 \hbar$/${\rm nm}$。