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

Abstract

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.