The orbital angular momentum of helical electrons and its implication on spin selectivity at chiral-achiral interfaces
Quantum numbers identify and differentiate between quantum states of a quantum system. The azimuthal or orbital angular momentum quantum numbers characterize wave functions that are invariant under discrete rotations. For a chiral system with screw symmetry, the rotational invariance is broken and the Bloch orbital angular momentum is generally not acknowledged. Here, we show that the wave functions of Bloch electrons in such a chiral system, denoted as helical electrons, are helical or vortex waves and, therefore, have well-defined orbital angular momentum along the screw axis. The collinear orbital-momentum locking imposed by the screw-induced orbital helicity leads to the orbital-selective transport as illustrated by tight-binding model calculations. We verify the helical states and orbital selectivity for two real chiral materials, namely, peptide helix and trigonal Se, by first-principles band structure calculations. Finally, we show that the interconversion between the orbital angular momentum and spin angular momentum at the chiral-achiral interfaces together with the orbital selectivity of the propagating helical electrons provide a fundamental principle for the chiral induced spin selectivity. Our understandings of the screw symmetry induced orbital angular momentum in chiral materials and the interplay between orbital angular momentum and spin angular momentum at the chiral-achiral interface paves a way for designing orbitronics and spintronics with chiral materials.