Chirality-Induced Spin Selectivity (CISS)

• Chirality Induced Spin Selectivity (CISS) is a quantum phenomenon where electrons traversing chiral environments acquire spin polarization without the need for external magnetic fields.
• The effect is modeled through effective Hamiltonians, multi-orbital tight-binding, and non-Hermitian dynamics that quantify geometry-enhanced spin–orbit coupling.
• Experimental and theoretical studies highlight CISS's potential in spintronics and catalysis while addressing challenges in accounting for many-body interactions and dynamical processes.

Chirality-induced spin selectivity (CISS) is a quantum phenomenon whereby electrons traversing chiral (i.e., handed) molecular or material environments acquire a pronounced, molecule- or crystal-dependent spin polarization in the absence of external magnetic fields. Experimental evidence for CISS spans organic molecules, chiral crystals, donor–acceptor complexes, and even engineered nanostructures. Theoretical descriptions of CISS incorporate effective Hamiltonian models, multi-orbital and many-body approaches, relativistic corrections, dynamical and open quantum system techniques, and topologically nontrivial frameworks. The underlying microscopic mechanisms remain under active investigation, with focus on spin–orbit coupling (SOC), geometric phases, non-Hermitian exchange, spin coherence generation, orbital Edelstein effects, and the interplay between coherent and incoherent processes.

1. Effective Hamiltonian Models and Chiral Geometry

Effective Hamiltonian frameworks provide an analytically tractable foundation for understanding CISS in chiral systems. The typical starting point is a separation of the electronic Hamiltonian into an orbital component and a spin–orbit interaction term: $$H_{\text{eff}} = H_0 + H_{\text{SOC}},\quad H_0 = \frac{p^2}{2m} + V(\mathbf{r}),\quad H_{\text{SOC}} = \lambda\, \boldsymbol{\sigma}\cdot (\mathbf{p} \times \nabla V(\mathbf{r}))$$ where $V(\mathbf{r})$ encodes the chiral molecular potential, $\lambda$ parameterizes SOC strength, and $\boldsymbol{\sigma}$ are the Pauli spin matrices (Geyer et al., 2020).

For helical molecules, further dimensional reduction leads to an effective one-dimensional Hamiltonian depending on the local twist angle $\theta(z)$: $$H_{\text{eff}} = \frac{p_z^2}{2m} + V(z) + \lambda\, [\sigma_x \sin\theta(z) - \sigma_y \cos\theta(z)] p_z$$ The SOC term introduces a position-dependent effective magnetic field tied to the molecular geometry, which produces spin-dependent phase accumulation during electron transport. The magnitude of spin polarization depends sensitively on $\lambda$, the geometric features of $V(\mathbf{r})$ (such as helical pitch and radius), and the effective mass $m$. Adiabatic perturbation theory is employed to handle the separation of fast (electronic) and slow (geometric) variables, yielding analytic expressions for the spin-dependent phase shift: $$\varphi_{\text{spin}} = \int dz\, \langle \psi_0(z) | H_{\text{SOC}} | \psi_0(z) \rangle / (\hbar v)$$ where $|\psi_0(z)\rangle$ is an eigenstate of $H_0$ and $v$ is the electron velocity.

2. Multi-Orbital and Channel Mixing in Chiral Junctions

Spin selectivity in transport through chiral molecules is fundamentally affected by the presence of multiple orbital channels and their mixing via SOC. Two-orbital tight-binding models, as developed in (Utsumi et al., 2020), explicitly incorporate intra-atomic SOC and the geometric structure of the molecule. In these models, SOC not only flips the electron spin but is concomitantly associated with changes in the orbital channel (e.g., between p_x and p_z orbitals).

The transmission problem is formulated in terms of scattering matrices, with the notable feature that time-reversal symmetric (two-terminal) devices with multi-channel mixing can still yield substantial spin polarization. This is despite Kramers’ degeneracy and Bardarson’s theorem, as the degenerate transmission eigenchannels may carry the same spin rather than canceling contributions. Explicit analytic expressions for the spin polarization, such as

$$P_{z,R} = \frac{6\sqrt{3} p z}{9 + 2z^2 - z^4 + |f_1(z)|^2}$$

demonstrate that the polarization reverses sign with the chirality parameter $p$, linking the effect directly to molecular handedness.

3. Dynamical, Many-Body, and Open-System Approaches

The CISS effect in real molecular systems often involves interplay between coherent evolution, many-body interactions, and dissipative processes. Lindblad-type master equations capture the dynamical evolution of the reduced density matrix for donor–bridge–acceptor systems: $$\hbar \frac{d\rho}{dt} = -i [H, \rho] + \Gamma (L_{AB} \rho L_{AB}^\dagger - \frac12\{L_{AB}^\dagger L_{AB}, \rho\}) + \Gamma_d \sum_{n,\mu} (L_{n \mu} \rho L_{n \mu}^\dagger - \frac12 \{L_{n \mu}^\dagger L_{n \mu}, \rho\})$$ where dephasing processes ($\Gamma_d$) induce a spin-conversion mechanism that enables accumulation of steady-state spin polarization at the acceptor (Zhang et al., 4 Sep 2025). The multi-orbital structure of the chiral bridge enables a combination of coherent inter-multiplet oscillations (enhanced by electron–electron correlations and exchange splitting) and incoherent transitions (including vibrational and environmental interactions), as shown in (Chiesa et al., 21 Jun 2024).

Spin coherence, rather than pure polarization, can also emerge when electron transfer is modeled using projection operator techniques (Nakajima–Zwanzig theory), leading to measurable quantum superpositions of singlet and triplet states, with the coherence phase locked to molecular handedness (Fay, 2021).

4. Role of Orbital Edelstein Effect and Relativistic Treatment

The orbital Edelstein effect has emerged as a key mechanism amplifying the observed spin polarization in CISS (Göbel et al., 7 Feb 2025). In chiral crystals or molecules, charge currents generate large orbital angular momentum due to the underlying geometry, which is then partially converted into spin polarization via SOC at interfaces or electrodes. Minimal models show that: $L_{1,z}(k) \propto \sin(k c/3)$ and the resulting orbital Edelstein susceptibility $\chi_z^{L_z}(E)$ can be orders of magnitude greater than the spin counterpart.

Ultimate theoretical consistency requires fully relativistic (4-component Dirac) DFT treatments, which incorporate both atomic and geometric SOC contributions and explicitly resolve spinor chirality: $$(i\gamma^\mu \partial_\mu - m)\psi = 0, \quad \gamma^5 = i\gamma^0 \gamma^1 \gamma^2 \gamma^3$$ The spatial variation of the chirality density (i.e., the expectation value of $\gamma^5$), and the transmission function’s dependence on molecular torsion/twist, confirm geometry-driven spin polarizations that exceed naive expectations from atomic SOC (Behera et al., 24 Dec 2024).

5. Non-Hermitian Quantum Exchange and Topological/Geometric Effects

A unified paradigm for CISS incorporates non-Hermitian quantum exchange in chiral systems. The absence of all mirror symmetries enforces electron “twin-pair” exchange, yielding a non-Hermitian term: $$H_{\text{eff}} = \frac{\hbar^2}{2m}p^2 + V - i\alpha(\boldsymbol{\sigma}\cdot \mathbf{p})$$ with broken $\mathcal{P}$ and $\mathcal{T}$ but preserved $\mathcal{PT}$ symmetry (Theiler et al., 9 May 2025). This scenario manifests spin–momentum locking and the non-Hermitian skin effect, with spin-polarized states localized at interfaces. For topologically nontrivial geometries, as in trefoil knot molecules, spatially varying local curvature directly yields a robust geometric SOC, giving ultra-high spin polarizations (up to 90%) (Sun et al., 27 Jul 2025).

Table: Physical origins and manifestations of CISS

Mechanism/Model	Signature	Materials/Systems
Effective 1D Hamiltonian	Geometry-enhanced SOC, spin-dependent phase	Organic molecules
Two-orbital tight-binding	Orbital–spin mixing, multi-channel degeneracy lifting	DNA, multi-orbital organics
Orbital Edelstein effect	Large orbital angular momentum, spin conversion via SOC	Chiral crystals, tellurium
Non-Hermitian exchange	Twin-pair exchange, skin effect, spin–momentum locking	Chiral molecules, materials
Geometric Berry phase/topology	Robustness, knot-induced SOC, ultra-high polarization	Trefoil knots, molecular knots

6. Experimental and Practical Implications

CISS has been observed in electron transmission, electron transport in junctions, and chemical reactions, with spin polarization exceeding what is predicted by single-particle SOC models, especially for systems with light elements (Evers et al., 2021). The experimental detection protocols vary: spin-resolved photoemission, magnetoresistance measurements, OOP-ESEEM EPR, and electron paramagnetic resonance have all been utilized. Phenomena such as violation of Onsager reciprocity (asymmetric magnetoresistance due to non-Hermitian skin effect and charge trapping (Zhao et al., 2022)), reversal of polarization with molecular handedness, and enantiosensitive locking of photoelectron spin and ion orientation (Flores et al., 28 May 2025) support a rich phenomenology.

Applications extend to spintronic devices (spin-filtering, spin-polarization control), current-induced magnetization for memory or logic, and chiral-selective catalysis and chemical synthesis. The effect is robust under room temperature and for atomically thin van der Waals materials, with twist-controlled spin selectivity exceeding 50% in twisted TMDs (Menichetti et al., 2023).

7. Challenges, Controversies, and Outlook

Several central challenges persist. The main quantitative puzzle remains the large size of observed spin polarization relative to predictions based on simple atomic SOC, as well as the proper accounting for non-equilibrium, dephasing, and many-body effects (Evers et al., 2021). The precise mechanism—whether primarily geometric SOC, many-body interactions, orbital Edelstein effects, or non-Hermitian exchange—is still debated across different contexts. Experimental results on temperature dependence, for example, can discriminate between vibrationally assisted mechanisms and models relying on interface "spinterface" magnetization (Alwan et al., 2022).

Current research is focused on extending theoretical frameworks to accommodate the observed non-equilibrium phenomena, multi-terminal and nonlinear transport, the role of molecular vibrations beyond thermal broadening (Miwa et al., 4 Dec 2024), and the emergence of spin coherence (Fay, 2021). Further, materials with engineered geometry (cavities, knots) and control over environmental coupling (dephasing, vibrational relaxation) are being developed to optimize and explore the effect in new regimes.

In sum, CISS is a paradigmatic example of the confluence of quantum geometry, SOC, many-body physics, and non-Hermitian dynamics, with implications for fundamental physics and future quantum technologies.