Geometric spin-orbit coupling and chirality-induced spin selectivity

Abstract

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 $0.01\hslash$ per $\mathrm{nm}$ when a charge current of $1\mu \mathrm{A}$ is applied.

7 pages, 2 figures

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• The Chiral Induced Spin Selectivity Effect -- What It Is, What It Is Not, And Why It Matters
• Emergence of chirality by multipole interconversion
• Mind the Gap: From Resolving Theoretical Foundations of Chiral(ity)-Induced Spin Selectivity to Pioneering Implementations in Quantum Sensing
• Should it really be that hard to model the chirality induced spin selectivity effect?
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