Advances Chiral-Induced Spin Selectivity Understanding Via Enhanced Spin-Orbit Coupling Models

Chiral-Induced Spin Selectivity (CISS) describes the surprising emergence of spin-polarized electron transport within chiral systems, even without applied magnetic fields. Researchers Ruggero Sala (Universita degli Studi di Pavia & IUSS), Sushant Kumar Behera (Universita degli Studi di Pavia), and Abhirup Roy Karmakar (Universit`a degli Studi di Milano), et al., now present a critical analysis of the microscopic origins of this effect, particularly in light-element materials where intrinsic spin-orbit coupling is weak. Their work highlights how molecular chirality, electric fields, and structural distortions can collectively amplify effective spin-orbit coupling, driving spin-dependent transport, and importantly, establishes a potential field-theoretic foundation for CISS. This research promises to unlock the potential of chiral nanomaterials as tunable platforms for nanoscale spintronics and the engineering of spin-selective phenomena.

This mini-review critically assesses existing models, evaluating their symmetry constraints, phenomenological assumptions, and adherence to Onsager reciprocity, providing a rigorous framework for future theoretical development. Experiments show that this link could position light-element chiral nanomaterials as highly tunable platforms for both probing and engineering spin-selective phenomena at the nanoscale, opening exciting avenues for materials science. The study establishes that understanding Spin dynamics and spin current, rather than solely charge transport, is central to fully grasping the intricacies of CISS, moving beyond traditional transport-based models like Green’s function approaches and the Landauer, Büttiker formalism.

Furthermore, the work highlights the importance of dynamical effects, demonstrating how low-frequency vibrational modulations of SOC in helical models can yield significant spin polarization, even in systems where time-reversal symmetry would normally prohibit it. A general theoretical framework, derived from relativistic quantum mechanics, inherently links spin and chirality, suggesting CISS may originate from fundamental quantum principles, a compelling proposition for physicists. New tools, such as the multipole expansion of relevant quantities, provide a powerful formalism for describing and unifying the diverse manifestations of CISS observed across various experimental setups. The research addresses key theoretical limitations, including the challenges posed by quasi-one-dimensional systems and the need to reconcile CISS observations with Onsager’s reciprocal relations, offering potential pathways to overcome these hurdles. Specifically, the team notes that multichannel transport, non-equilibrium conditions, and dynamical SOC all lift the constraints imposed by single-channel models, paving the way for more realistic and predictive theoretical models. This detailed analysis aims to clarify the conceptual landscape and pinpoint promising directions for future research, ultimately striving towards a unified theoretical framework that fully explains and harnesses the power of CISS for advanced technological applications.

CISS Calculations with Coherent and Incoherent Scattering

These calculations meticulously defined a central region, the chiral molecule, connected to metallic leads, enabling computation of charge currents under steady-state conditions using Green’s function-based scattering theory and, occasionally, Density Functional Theory (DFT) Hamiltonians. To address limitations of purely phase-coherent scattering, the research team introduced both phase-breaking and inelastic scattering via Büttiker probes and phenomenological leakage terms, strategically augmenting the models to better reflect real-world conditions. The study pioneered two primary Hamiltonian construction approaches: ab initio density functional theory (DFT) and parameterized tight-binding (TB) models. DFT-based Non-Equilibrium Green’s Function (NEGF) calculations, while computationally intensive, naturally incorporated key screening effects and effectively broke the time-reversal invariance of the self-consistent Hamiltonian, providing a physically grounded foundation.

Conversely, TB models offered greater parameter control, facilitating exploration of qualitative CISS aspects; both approaches benefited from the inclusion of virtual probes through phenomenological self-energy terms. Researchers also explored wavefunction scattering-matrix formalisms, though adoption remained limited due to concerns regarding applicability in systems lacking inelastic scattering. Furthermore, the work developed a perturbative NEGF model, introduced by Dalum and Hedegard, which captures CISS responses through an auxiliary axial vector describing spin polarization of scattered electrons. Initial implementations utilized idealized TB models of twisted polyacetylene, motivating a future goal of a more realistic, ab initio implementation of the vector formalism.
The team demonstrated that magnetization can emerge under non-equilibrium conditions, finite bias, even without ferromagnetic electrodes, challenging conventional assumptions about time-reversal invariance. Zollner et al’s work revealed that spin-orbit coupling introduces “imaginary” spin-dependent terms in the Hamiltonian, crucial for maintaining Hermiticity and enabling non-zero spin polarization alongside inversion symmetry. A careful symmetry analysis showed that longitudinal symmetry planes impose no constraints on transverse spin polarization, while enforcing the vanishing of the longitudinal component, unless the molecular junction possesses a longitudinal symmetry axis. This configurational averaging allows spin polarization to emerge in chiral molecules, as their accessible configurational space is intrinsically symmetry-broken, a key finding supported by nanoscale scanning probe measurements and averaged behaviour of chiral media.

CISS efficiency linked to timescale matching

Experiments reveal that CISS arises from the entanglement of spin and spatial degrees of freedom, functioning as a dynamic form of spin filtering where selectivity emerges during transport itself. The team measured that the efficiency of this filtering is contingent on the interplay between the spin precession frequency, determined by SOC, and the electron’s dwell time within the chiral medium. Results demonstrate that only when these timescales are favorably matched does robust dynamic spin polarization manifest, with environmental interactions potentially enhancing or suppressing the effect depending on their strength and temporal structure. Modeling approaches, including time-dependent NEGFs (TD-NEGF), high-dimensional wave-packet propagation, and stochastic Schrödinger equations, have shown that even weak SOC can induce significant spin polarization when combined with molecular asymmetry and partial coherence.

The work confirms that CISS reflects a fundamentally dynamical mechanism where spin filtering evolves over time under the influence of both coherent and dissipative interactions. Researchers employed time-dependent DFT, particularly in its four-component relativistic form, as an ab initio framework for describing SOC and chiral electronic structure. To model non-equilibrium charge transport and spin decoherence, central to CISS dynamics, NEGF-based transport simulations were extended to include spin degrees of freedom and SOC, allowing computation of spin-resolved currents through molecular junctions under bias. Complementary open quantum system approaches, such as Lindblad formalisms and Redfield theory, model the interaction of spins with thermal and vibrational baths, capturing relaxation and dephasing dynamics.

Recent developments integrate machine learning with quantum dynamics simulations to efficiently explore molecular design spaces and predict spin-filtering behavior across diverse chiral scaffolds. Within this formalism, the expectation value of the γ5 matrix reduces to the helicity operator, acting as a pseudoscalar quantity that is P-odd and T-even, mirroring the definition of true chirality. The complete multipole representation (CMR) framework systematically classifies electronic degrees of freedom, including charge, spin, and orbital angular momentum, extending conventional multipoles with electric toroidal and magnetic toroidal components crucial for representing chiral phenomena. Future research should focus on integrating phenomenological models with predictive ab initio approaches, alongside advancements in current- and spin-current density functional theory. Multiscale simulations combining relativistic quantum chemistry with open-system dynamics are also needed to fully capture coherence and decoherence effects. These combined efforts promise a quantitative, symmetry-based foundation for designing chiral platforms for spintronics, quantum information, and catalysis.