Orbital Angular Momentum Textures and Currents in a Discrete Helix: Equilibrium and Linear Response

TL;DR

This paper introduces a minimal model showing how chirality alone can generate orbital angular momentum textures and currents in a helical chain, revealing new mechanisms for spin polarization and orbital responses without relying on atomic spin--orbit coupling.

Contribution

It demonstrates that chirality is sufficient to produce orbital angular momentum textures and responses in one-dimensional systems, expanding understanding of chiral-induced orbital phenomena.

Findings

Chirality generates momentum-dependent orbital textures without atomic spin--orbit coupling.

Equilibrium orbital textures vanish by parity, but currents and end magnetization can persist.

Orbital-to-spin transduction leads to a strong spin response, larger than conventional mechanisms.

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 $(p_r,p_\phi,p_z)$, 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 $(p_z,p_r)$ and $(p_r,p_\phi)$ 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-current 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. The resulting spin response is controlled by orbital overlap scales much larger than the bare relativistic spin--orbit scale, 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.