Chirality-Induced Orbital Selectivity

• CIOS is a phenomenon in which chiral environments selectively filter electron orbital angular momentum through geometric spin–orbit coupling.
• The effect arises from strong linear–orbital coupling, where curvature and pitch of the chiral structure dominate over conventional spin–orbit interactions.
• CIOS has practical implications for molecular spintronics, quantum information devices, and chiral sensors by enabling robust and tunable electron transmission.

Chirality-Induced Orbital Selectivity (CIOS) refers to the phenomenon whereby electron transport through a chiral environment results in selective transmission or polarization of electronic orbital angular momentum (OAM) states, with the selectivity—and even its sign—strictly controlled by the handedness of the chiral structure. In CIOS, the chiral symmetry of the medium imposes geometric constraints and couplings that favor certain orbital channels over others, resulting in robust enantiospecificity and pronounced consequences for electron dynamics, particularly in molecular electronics, spintronics, and orbitronics.

1. Fundamentals of CIOS: Geometric Origin and Core Mechanism

CIOS arises from the interplay between structural chirality and the orbital degrees of freedom of an electron. The essence of the effect is encapsulated by the observation that motion through a helical or generally chiral potential imparts a geometrically induced coupling between linear and angular momentum. In the case of a helical molecule, the electron is confined to a space curve whose curvature $\kappa$ and binormal vector $\mathbf{B}$ generate an effective geometric spin-orbit coupling (SOC), described by the Hamiltonian

$$H_\mathrm{t}^{(1)} = \frac{1}{2m}\left[p_s + \frac{\hbar\kappa}{2}\left(\sigma \cdot \mathbf{B}\right)\right]^2,$$

where $p_s = -i\hbar\partial_s$ is the canonical momentum along the curve, $\sigma$ is the spin vector, and $m$ is the electron mass (Shitade et al., 2020). The effective gauge term $A_s = (\hbar\kappa/2)(\sigma\cdot\mathbf{B})$ acts to directly couple the orbital and spin degrees of freedom to the local chiral geometry. Notably, this geometric SOC is an order of magnitude larger ($O(m^{-1})$) than atomic SOC ($O(m^{-2})$), making curvature-driven effects dominant in systems of light elements.

Beyond strictly one-dimensional models, general three-dimensional treatments show that any chiral potential whose transverse structure varies with the axial coordinate (e.g., the helical displacement $x = R\cos(z/P)$, $y = R\sin(z/P)$) leads to a term in the Hamiltonian of the form

$$[p_z + i\beta \left(e^{iz/P}(c - d^\dagger) - e^{-iz/P}(c^\dagger - d)\right)]^2/(2m),$$

where $c, d$ are bosonic ladder operators for OAM and $\beta$ measures the strength of linear–orbital coupling (proportional to $R/P$ and $\omega$, the transverse confinement frequency) (Cho et al., 9 Sep 2025). Any change in OAM (by $\pm\hbar$) is accompanied by a shift in longitudinal momentum, governed by the pitch $P$, enforcing a strict coupling of orbital transitions to electron propagation.

2. Enantiospecific Transmission and Orbital Polarization

A central manifestation of CIOS is the enantiospecific transmission of electrons with a given OAM. The transition probabilities between OAM states during passage through a chiral region exhibit pronounced selectivity: electrons incident in state $|1,0\rangle$ (with $+\hbar$ OAM, for example) preferentially convert to $|0,0\rangle$ via transitions that increase their longitudinal momentum by $\hbar/P$, enhancing their capacity to overcome potential barriers. This effect is inverted for $|0,1\rangle$ ($-\hbar$ OAM) states, whose transmission is suppressed under identical conditions (Cho et al., 9 Sep 2025). The selection rules arise from the necessity to conserve both energy and momentum in the scattering process, with the geometric (chirality-induced) coupling dictating which orbital transitions are accessible.

In coupled multi-stranded helices (such as double-stranded DNA), the change of the binormal vector across strands renders the effective SOC, and hence the orbital selectivity, exquisitely sensitive to handedness. This leads to mirror–antisymmetric transmission features for right- and left-handed molecules (Shitade et al., 2020, Utsumi et al., 2020).

3. Linear–Orbital Coupling Versus Spin–Orbit and Spin–Phonon Interactions

Linear–orbital coupling, representing the shift in longitudinal momentum accompanying OAM transitions, is found to be significantly stronger than spin–phonon and bare spin–orbit mechanisms under realistic parameters. For instance, with $R \sim 1\,\mathrm{nm}$, $P \sim 0.5\,\mathrm{nm}$, and $\omega \gtrsim 0.1\,\mathrm{eV}$, the resulting energy scale for the linear–orbital term is on the order of tenths of an electron volt. By contrast, the typical spin–orbit interaction in organic molecules lies in the range of several meV, and spin–phonon energies scarcely exceed $0.01$ eV (Cho et al., 9 Sep 2025). Consequently, CIOS driven by linear–orbital coupling dominates the electron dynamics and transmission properties.

In models where electrons tunnel through chiral molecules, the differential decay rates for OAM (and thus spin, when entanglement exists) are expressed as

$T_\sigma \sim e^{-2\kappa_\sigma a},$

with $\kappa_\sigma$ determined by orbital- and spin-dependent couplings—including the chiral modulation of overlaps and potential barriers (Mena et al., 19 Jun 2024). This formalism quantitatively links the magnitude of CIOS to molecular parameters and the electronic structure.

4. Robustness, Scaling, and Dependence on Molecular Structure

CIOS exhibits multiple robustness features:

• Length scaling: The difference in transmittance between OAM states systematically increases with the length of the chiral region, reaching orbital polarizations up to $80\%$ for several turns of the helix-shaped potential (Cho et al., 9 Sep 2025).
• Resistance to static disorder: Simulations incorporating random displacements of the confining Gaussian potentials show that the magnitude of selectivity (e.g., as measured by $\Delta T$) remains almost unchanged up to disorder strengths on the order of $0.1$ nm.
• Dependence on chirality: The magnitude and sign of orbital selectivity are strictly governed by the handedness parameters (helix pitch $P$, sign of torsion, or the chirality index $\chi$). Reversal of chirality instantly reverses the direction of induced polarization (Cho et al., 9 Sep 2025, Liu et al., 2020, Hagiwara et al., 27 Oct 2024).

5. Conversion to Spin Selectivity and Connection to CISS

Although the intrinsic (bare) spin–orbit coupling may be weak, the strong CIOS effects can be converted into spin selectivity if there exists an initial correlation between electron spin and OAM. For example, if the injection process prepares electrons with spin aligned to their OAM (spin–OAM entangled states), then the chiral environment’s robust transmission filter for OAM will produce large net spin selectivity in the output (Cho et al., 9 Sep 2025). This mechanism underlies observations in both molecular (Liu et al., 2020, Utsumi et al., 2020) and solid-state (Hagiwara et al., 27 Oct 2024, Yang et al., 2023) systems, and offers a geometric perspective that complements traditional spin-based models.

In the experimental context where a chiral molecule is interfaced with a heavy-metal electrode, the orbital polarization produced by CIOS is converted via strong SOC in the electrode to a measurable spin polarization (CISS), highlighting the CIOS effect as the microscopic precursor to detectable spin filtering (Adhikari et al., 2022).

6. Technological Implications and Applications

The pronounced CIOS effect, its tunability via geometry (pitch, radius, length), and robustness to disorder and temperature have direct relevance for:

• Molecular spintronics and orbitronics: Exploiting OAM-selective transport for information processing, memory elements, and spin–orbit torque oscillators.
• Quantum information science: Enabling quantum state encoding and manipulation by injecting or selecting specific OAM modes in chiral quantum wires or molecular devices.
• Enantioselective electron transport: Designing sensors and separation devices that leverage enantiospecific OAM filtering (Cho et al., 9 Sep 2025).
• Biosensing and catalysis: Harnessing selective transmission properties in chiral environments for detection and control of molecular processes.
• Optoelectronics: Inducing or detecting OAM-polarized currents via engineered chiral environments, with potential extensions to circularly polarized light emission or detection.

These implications are strengthened by the demonstrated scalability of CIOS with molecular length and chirality, and its resilience in the presence of realistic disorder and at energy scales relevant for room-temperature operation.

7. Future Directions

Research continues to explore:

• The interplay of CIOS with electron–phonon interactions and decoherence, establishing the requirements for robust OAM polarization in open (dissipative) environments (Mena et al., 19 Jun 2024, Fransson, 1 Jan 2025).
• Extensions of the CIOS paradigm to solid-state chiral crystals (e.g., CoSi, RhSi, trigonal Se) where CIOS governs the topology of the electronic band structure and the appearance of chirality-driven multifold fermions and helicoid Fermi arcs (Hagiwara et al., 27 Oct 2024, Yang et al., 2023, Brinkman et al., 3 Apr 2024).
• The impact of CIOS on electron–electron correlations, coupled spin–orbital transport, and its role as a precursor for novel nonequilibrium and topological phenomena.

Advances in wave-packet dynamics simulations, angle-resolved photoemission (CD-ARPES), and enantiosensitive electron spectroscopy are expected to further clarify the role of CIOS in quantum materials and molecular systems, and to inform the engineering of next-generation devices exploiting chirality at the nanoscale (Chen et al., 3 Sep 2025).