Spin‐Filtering in a p ‐Orbital Helical Atomic Chain

We theoretically analyze spin filtering in two-terminal systems, induced by the spin-orbit interaction (SOI), as a possible origin of the “chirality-induced spin selectivity” (CISS) effect observed experimentally in chiral molecules, such as DNA. Due to Bardarson’s theorem, spin filtering cannot be realized in a molecule containing one orbital-channel. How-ever, when two orbitals are involved, SOI can induce spin filtering in a molecule coupled to two terminals without brak-ing time-reversal symmetry. In particular, we provide an example of a 4 × 4 reflection matrix for a spinful electron passing through a molecule containing two orbital-channels, which complies with Bardarson’s theorem and produces a finite spin conductance. As a microscopic toy model realizing a single strand of DNA, we consider a p -orbital helical atomic chain with intra-atomic SOI’s and a strong crystalline field along the helix. This model exhibits two-orbital spin filtering: For various parameters preserving the helical symmetry, the model hosts spin asymmetric states carrying pairs of up and down spins propagating in opposite directions. The typical energy scale of the helical states is the product of the intra-atomic SOI and the curvature. The large value of this energy identifies our model as a likely candidate to explain the CISS in organic molecules. same helix and thus the intra-atomic SOI is sufficient for the spin-filtering. In our simple p -orbital helical atomic chain, the typical energy scale of the helical states is approximately the intra-atomic SOI times the curvature of the helix. The intra-atomic SOI is typically larger than the inter-atomic SOI induced by the mixing between π - and σ -bands and thus would be a likely candidate for explaining the CISS effect.