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. However, when two orbitals are involved, SOI can induce spin filtering in a molecule coupled to two terminals without braking time-reversal symmetry. In particular, we provide an example of a (Formula presented.) 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 spin filtering mechanism is associated with the intra-atomic SOI, which would be larger than the inter-atomic SOI. In this respect, the present model may be a more likely candidate for the CISS in organic material than other models associated with the inter-atomic SOI.