Transport Hamiltonians for helical spintronics: Derivation from symmetries

Symmetry alone imposes a sharp constraint on spin-dependent transport in helical structures: for an ideal double helix with equivalent strands, tunneling between strands is necessarily spin-flipping, while spin-conserving inter-strand hopping is symmetry-forbidden. We elevate this statement into a constructive modeling program by deriving tight-binding transport Hamiltonians directly in real space from the line-group symmetries of single and double helices, supplemented by time-reversal invariance. The result is a symmetry-complete nearest-neighbor parametrization for mobile π-like (p_z) orbitals: intra-strand motion admits both spin-preserving and spin-flip channels, whereas the inter-strand sector of the symmetric double helix is purely spin-active. We further provide a microscopic Slater-Koster interpretation of the allowed couplings, identifying s-p-d pathways in which atomic spin-orbit interaction cooperates with the intrinsic inversion-asymmetry field of the helix, so that Rashba-like terms emerge as an internal consequence of chirality rather than as an externally imposed ingredient. Finally, we give compact Bloch Hamiltonians and the corresponding momentum-dependent effective spin-orbit fields that determine band splittings and spin textures, establishing a controlled baseline for parameterization and quantum-transport modeling of DNA-like helices.