Orbital angular momentum textures and currents in a discrete helix: Equilibrium and linear response

Recently, nonequilibrium orbital angular momentum in low-dimensional systems has attracted renewed attention. Here, we introduce a minimal three-orbital tight-binding model for a single helical chain and show that chirality alone generates a momentum-dependent orbital-angular-momentum texture through Slater-Koster hybridization in the local basis (pr, pϕ, pz), without requiring atomic spin-orbit coupling. In the single-helix geometry, the radial orbital texture vanishes identically, while the azimuthal and longitudinal components remain finite and arise from the odd-in-momentum (pz, pr) and (pr, pϕ) sectors. As a result, the equilibrium average orbital texture vanishes by parity, although persistent-like orbital angular momentum currents may still exist and imply chirality-dependent end magnetization in a finite helix. Under an applied longitudinal electric field, the system develops a finite orbital Edelstein response, whereas the projected longitudinal orbital conductivity vanishes in the linear regime by parity. When spin degrees of freedom are included, the orbital texture acts as a source of spin polarization through orbital-to-spin transduction. Instead of being limited by the weak, natural spin-orbit coupling of individual atoms, the overall spin response is driven by the much stronger interactions of overlapping molecular orbitals, making it a stronger candidate for spin injection than the conventional spin Edelstein mechanism. These results identify chirality as the minimal microscopic ingredient for generating orbital angular momentum response in one-dimensional systems and support an orbital route to spin selectivity in chiral conductors.