Tunneling amplifies chirality-induced spin selectivity and explains its current-direction invariance

Abstract: We propose a minimal model for chirality-induced spin selectivity (CISS) in dc transport through insulating chiral molecules, based on quantum tunneling and interaction-induced spin splitting. As a concrete realization of the latter, we consider a weak Zeeman interaction of the particle spin with the current-induced magnetic field, recently shown to occur in helical molecules. We show that quantum tunneling, combined with dissipation, amplifies the effect, so that even such a small spin-dependent perturbation can yield spin polarizations on the order of 100\% across a wide range of applied bias voltages. Furthermore, our tunneling scenario naturally reproduces the characteristic CISS symmetry of the current-voltage dependence -- namely, the invariance of the spin-polarization sign under reversal of the current direction -- while fully respecting Onsager's reciprocity relations.

• The paper demonstrates that tunneling amplifies weak Zeeman-induced spin splitting to achieve near 100% spin polarization in chiral molecules.
• The model uses WKB and Landauer-Büttiker analyses to quantitatively reproduce experimental data and explain the invariance of spin polarization upon current reversal.
• The study reveals that incorporating dissipation broadens the voltage range of significant spin polarization, emphasizing the importance of non-linear transport effects.

Tunneling-Enhanced Chirality-Induced Spin Selectivity: A Minimal Model Approach

Introduction

The paper "Tunneling amplifies chirality-induced spin selectivity and explains its current-direction invariance" (2606.17823) investigates the microscopic foundations of the chirality-induced spin selectivity (CISS) effect observed in electronic transport through insulating chiral molecules. Existing literature reports unexpectedly large spin polarization (SP) in such systems, often approaching 100%, with a notable invariance of the SP sign upon reversal of the current direction. The paper sets out to resolve the mechanistic deficiency of existing theoretical approaches in accounting for both the magnitude of SP and its peculiar current-direction symmetry, while reconciling the effect with fundamental constraints such as Onsager’s reciprocity.

Model Formulation and Key Mechanisms

The authors present a minimal theoretical framework for the CISS phenomenon, focusing on electron transport in the tunneling regime through insulating chiral molecules. The model incorporates interaction-induced spin splitting, concretely realized as a Zeeman effect from self-induced magnetic fields generated by the tunneling current in a helical geometry. This mechanism is motivated by recent ab initio calculations and analytical estimates indicating that local magnetic fields induced by current in chiral molecules could reach the Tesla scale.

Crucially, the smallness of the Zeeman perturbation (order $10^{-4}$ eV) is not a limiting factor due to the exponential sensitivity of tunneling probabilities to variations in the barrier properties. In contrast to single-particle approaches, which cannot yield appreciable SP due to Kramers' degeneracy and time-reversal symmetry, the authors demonstrate that current-induced symmetry breaking via interaction effects opens a channel for substantial spin selectivity.

Amplification of Spin Polarization via Tunneling

By recasting the transport through the molecule as a 1D quantum tunneling problem, the model identifies the key scaling relation: the ratio of the molecule length $L$ to the characteristic mean free path associated with the Zeeman-induced splitting determines the maximum achievable SP. For typical parameters, this leads to the possibility of nearly 100% spin polarization across chiral molecular films of experimentally relevant dimensions. The detailed WKB analysis and self-consistent Landauer-Büttiker calculations confirm that even a weak spin splitting, when amplified by long tunneling distances, can account quantitatively for the giant CISS signals.

Another technically important aspect is the inclusion of dissipation, represented in the model by a spin-independent resistive element at the tip-molecule interface. This dissipative environment markedly broadens the bias window over which large SP persists, resolving the previously unexplained experimental observation of SP over finite, experimentally accessible voltage ranges. The SP enhancement mechanism depends primarily on the tunneling amplification of spin splitting, while the resistor primarily regulates the voltage profile across the molecular barrier.

Explanation of Current-Direction Invariance and Onsager Reciprocity

The model naturally reproduces the current-direction invariance of the SP observed in CISS experiments. Under bias reversal, the current and thus the self-induced magnetic field flip sign, as do the spin-resolved energy levels (e.g., HOMO or LUMO, depending on the bias). This robustly preserves the sign of the spin polarization. The authors emphasize that this symmetry does not violate Onsager's reciprocity, as the strong SP occurs only in the non-linear response regime outside the scope of linear conductance-based constraints.

Numerical Results and Temperature Effects

Calculated I–V characteristics reproduce qualitative and quantitative features of experiment: (i) 100% spin polarization occurs for realistic molecular lengths and current-induced fields, and (ii) dissipation extends the voltage range of appreciable SP. The scaling with molecule length and Zeeman interaction strength closely matches analytic predictions.

Finite temperature analysis reveals thermal broadening-induced suppression of SP as thermally excited electrons initiate transport above the tunneling barrier. The model predicts a temperature dependence of SP, in agreement with the heterogeneous experimental reports on the robustness of CISS at elevated temperatures. The explicit formalism enables further generalizations, such as the inclusion of inelastic tunneling and environmental effects.

Theoretical and Practical Implications

The proposed minimal tunneling model successfully bridges the discrepancy between the large experimentally measured SP in CISS and the much smaller values predicted in single-particle plus spin–orbit coupling scenarios. It underscores the necessity of incorporating interaction-induced spin splitting and non-equilibrium effects into models of molecular spintronics. The inclusion of dissipation highlights the relevance of molecular junction architecture, specifically distinguishing molecular films from rigid single-molecule junctions where CISS tends to be absent.

On the experimental front, the model provides clear testable signatures: the scaling of SP with length, bias window broadening by dissipation, and the direction-invariance of SP. It also points to the potential of engineering molecular spintronic devices by manipulating interface dissipation and controlling vibrational coupling.

Theoretically, the insights gained underscore the need for a non-linear response approach to molecular spintronic effects, and set the stage for incorporating more intricate correlation mechanisms and inelastic phenomena. The analysis delineates the parameter regimes in which interaction-induced effects rather than intrinsic spin–orbit coupling dominate spin selectivity.

Conclusion

This work elucidates how quantum tunneling through insulating chiral molecules, together with self-induced magnetic fields and moderate dissipation, can fully account for the phenomenology of the CISS effect, including its magnitude and symmetry properties. The treatment resolves major outstanding issues in the theoretical understanding of CISS, provides explicit criteria for the observation of strong spin polarization, and suggests that similar amplification mechanisms may arise from other types of interaction-induced spin splitting. The framework paves the way for further explorations of correlation-driven spin phenomena in molecular electronics and the rational design of spin-selective nanostructures.