Ballistic Spin and Chirality Transport

• Ballistic spin and chirality transport is the coherent propagation of spin and chiral properties in low-dimensional systems, driven by spin–orbit coupling and chiral symmetry.
• The interplay of SOC, molecular geometry, and chiral symmetry leads to spin-dependent velocity asymmetries that enable effects like chirality-induced spin selectivity and chirality Hall responses.
• Experimental platforms in chiral molecules, topological insulators, and quantum wires showcase potential applications in spintronics and quantum information transport.

Ballistic spin and chirality transport refers to the quantum-coherent propagation of spin and chiral (handedness-sensitive) degrees of freedom through low-dimensional conductors—such as helical molecules, chiral crystals, quantum wires, topological edge states, or strongly correlated spin chains—in the absence of significant inelastic (scattering or dephasing) events. In this regime, the interplay of structural chirality, spin–orbit coupling (SOC), and material symmetry can induce robust, direction- and spin-dependent filtering: certain spin or chirality channels propagate faster or more efficiently, resulting in net spin-polarized currents and chiral Hall responses even without magnetic fields. This mechanism underlies key phenomena such as the chirality-induced spin selectivity (CISS) effect in organic systems, the emergence of chiral edge states in topological insulators and semimetals, and the ballistic motion of spin–chirality solitons in synthetic quantum matter.

1. Microscopic Hamiltonians and Chiral Symmetry

Across organic and inorganic systems, ballistic spin–chirality transport arises from a class of Hamiltonians combining kinetic, spin–orbit, and chiral-symmetry-breaking terms. In chiral molecules, the minimal microscopic Hamiltonian typically includes nearest-neighbor hopping with a helical geometric modulation and an intrinsic or emergent SOC: $$H = \sum_{i,j,s} t_{ij}\,c_{i,s}^\dagger c_{j,s} + \sum_{i,j,s,s'} i\,\lambda_{\rm SO}\; (d_{ij}\cdot \vec{\sigma}_{s,s'})\,c_{i,s}^\dagger c_{j,s'} + \mathrm{h.c.}$$ where $t_{ij}$ is the helical hopping, $d_{ij}$ denotes bond vectors encoding the handedness, and $\vec{\sigma}$ are the Pauli matrices. In topological materials, the generic Weyl Hamiltonian is

$$H_\tau(\vec{k}) = \tau(v_x \sigma_x k_x + v_y \sigma_y k_y + v_z \sigma_z k_z)$$

with $\tau = \pm 1$ labeling chiral nodes. Chiral symmetry and noncentrosymmetric geometry are essential: in helical molecules, the absence of inversion produces effective subset selection in the transmission eigenchannels according to pseudo-angular momentum (PAM) (Wang et al., 2023); in 2D systems, the tilt of a chiral molecular dipole ($\phi \ne 0$) breaks mirror symmetry and enables enantiospecific Hall and spin-flip processes (Alhyder et al., 18 Mar 2025).

2. Spin–Chirality Coupling, Group Velocity Asymmetry, and CISS

A defining feature is the emergence of spin- and chirality-dependent group velocities. In a helical environment, SOC lifts the degeneracy between spin-propagation channels, with the energy dispersion

$$E_\pm(k) = \varepsilon_0 - 2t_0 \cos(k d) \pm 2\lambda_0 \chi^z \sin(2 k d)$$

and group velocities

$$v_{g,\pm} = (2 t_0 d/\hbar) \sin(k d) \mp (4 \lambda_0 \chi^z d/\hbar) \cos(2 k d).$$

This difference directly produces a "velocity asymmetry": spin-up and spin-down electrons traverse a chiral molecule with distinct speeds, leading to unequal transmitted spin densities and ballistic spin polarization—precisely the fundamental mechanism of the CISS effect (Stuermer et al., 31 Oct 2025, Hoff et al., 2021).

In Weyl semimetals, the phase-space Berry curvature $\Omega_k$ generates an anomalous velocity $$\dot{\mathbf{r}} = \nabla_k \varepsilon - \dot{\mathbf{k}} \times \Omega$$, resulting in opposite direction-dependent lateral shifts for left- and right-chiral carriers—a chirality Hall effect (Yang et al., 2015).

3. Ballistic Spin Filtering, Quantum Interference, and Topological Protection

Spin-polarized transport in the ballistic regime derives from the suppression of backscattering (spin-momentum locking/topological protection) and the conversion of chiral, or pseudo-angular-momentum (PAM), polarization into spin polarization at symmetry-broken interfaces. In screw-symmetric lattices, electronic eigenstates are quantized by their PAM $j = m + s$ (with $m$ orbital and $s$ spin contributions) (Wang et al., 2023). At interfaces between chiral and achiral materials, wave-function matching rules ensure that only the correct $j$ channels couple, transducing bulk chiral selectivity into spin-polarized outputs even in the absence of intrinsic atomic SOC.

Coherent effects such as quantum interference (QI) and dephasing play subtle roles. In helix-based molecular devices, the presence of multiple interference paths results in energy-dependent constructive (CQI) or destructive (DQI) quantum interference, which, when combined with CISS, yields spin-selective anti-resonances and resonance lineshapes in the conductance (Chen et al., 2023). Properly tuned dephasing suppresses time-reversal-imposed cancellations, amplifying spin filtering.

4. Interface Engineering and Spin Manipulation

The local atomic geometry and orbital occupancy at chiral interfaces critically determine the fate of spin coherence and selectivity. For example, in coupled helical chains, the availability of an open $p_z$ orbital at the interface allows for efficient spin-flip transmission via off-diagonal elements of $\mathbf{L} \cdot \mathbf{S}$; in geometries supporting filled or localized orbital states, spin-flip is suppressed and pure spin-preserving ballistic transport results (Matsubara et al., 15 Jan 2025). Rational design of the interfacial bonding and atomic registry can thus switch a material between spin-filter, spin-valve, or spin-preserving operation—without the need for external magnetic fields.

In inorganic high-SOC nanowires, such as Bi(111), ballistic chiral edge states can be manipulated with moderate Zeeman fields to induce 0–$\pi$ transitions or anomalous ($\varphi_0$-) Josephson effects, providing direct experimental control over spin–chirality–locked transport (Murani et al., 2016).

5. Geometric, Relativistic, and Topological Mechanisms

On the theoretical side, both relativistic (Dirac-level) and geometric/Berry-phase–mediated SOC contribute to spin–chirality transport. Fully relativistic Dirac–Kohn–Sham (DKS) theory yields a chirality density $\chi(\mathbf{r}) = \Psi^\dagger \gamma^5 \Psi$ that tracks molecular handedness, and under external fields controls the angle-dependence of spin filtering; the maximal spin polarization arises for moderate molecular twist angles and increases linearly with applied longitudinal fields (Behera et al., 24 Dec 2024). In Weyl semimetals and topological insulators, Berry curvature and angular-momentum conservation encode universal transverse (out-of-plane) shifts in transmission and reflection, distinguishing left- and right-chiral carriers (Yang et al., 2015).

6. Experimental Realizations and Dynamical Signatures

Ballistic spin–chirality transport is directly observed in quantum devices and synthetic platforms, including:

• Chiral molecular monolayers exhibiting robust spin-filtering and gate-tunable magnetic signal pulses, arising from group-velocity asymmetry and persistent steady-state spin polarization (Stuermer et al., 31 Oct 2025).
• Josephson junctions through Bi nanowires, where current-phase relation (CPR) analysis reveals sawtooth behavior characteristic of long ballistic channels (Murani et al., 2016).
• Polariton condensate rings that display coherent ballistic propagation, spin precession, and zitterbewegung-type motion due to effective spin–orbit splitting, confirming the group-velocity-based description (Yao et al., 2022).
• Synthetic spin Kitaev chains engineered by Floquet protocols, where spin excitations with $S^x$ and $S^y$ polarization propagate chirally in opposite directions; in the large-$S$ limit, this maps to nonlinear Hatano–Nelson soliton dynamics with controllable directionality and field-tunable transport (Lv et al., 23 Aug 2025).
• 1D Heisenberg spin chains in real materials (Cu-PM), where $\mu^+$SR experiments detect ballistic spin transport at low temperature, while structurally chiral (non-integrable) chains show spin diffusion, reflecting the sensitivity of chirality transport to integrability and magnetic order (Huddart et al., 2020).

7. Theoretical Predictions, Scaling, and Implications

Table: Central mechanisms and key results for ballistic spin–chirality transport

System	Core Mechanism	Notable Result/Scaling
Chiral molecules	SOC + helical geometry	Spin polarization $\sim \sin\theta$; $P \propto L$
Topological systems	Berry curvature, PAM	Chirality Hall effect; quantized lateral shifts
Chiral interfaces	Orbital selection, SOC	Switchable spin-flip vs. spin-preserving response
Sine-Gordon chains	Integrability, solitons	Ballistic vs diffusive crossover in spin transport
Synthetic spin models	Floquet/nonlinear dynamics	Chiral solitons, field-tunable velocity

Predictions include the exponential approach to full spin selectivity with molecular length, sign reversal of polarization with handedness or bias, and the role of the SO-induced gap in suppressing backscattering (Medina et al., 2015, Wang et al., 2023). In the presence of geometric or Berry-phase–type SOC, the magnitude of spin-polarized currents scales with torsion, twist angle, and the non-adiabatic Aharonov–Anandan phase, while interface and device design offers practical routes for controlling transport channels, enantioselectivity, and topological protection.

Developments in quantum transport theory and synthetic quantum matter are expected to further elucidate and exploit these mechanisms, with applications ranging from molecular spintronic devices to quantum computation, enantiosensitive detection, and robust quantum information transport.

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Key references: (Yang et al., 2015, Stuermer et al., 31 Oct 2025, Wang et al., 2023, Behera et al., 24 Dec 2024, Lv et al., 23 Aug 2025, Matityahu et al., 2015, Alhyder et al., 18 Mar 2025, Murani et al., 2016, Matsubara et al., 15 Jan 2025, Chen et al., 2023, Yao et al., 2022, Huddart et al., 2020, Hoff et al., 2021, Medina et al., 2015).