Theory of nonlinear spin transport in chiral conductors

Abstract: The chirality-induced spin selectivity (CISS) effect, discovered by Naaman and collaborators in 1999, describes the emergence of a finite spin polarization in response to current flow through a chiral electronic system. While extensive experimental studies have verified the presence of CISS in molecular systems and, more recently, in chiral materials, a complete microscopic understanding of this effect remains elusive. In this work, we propose a theoretical framework linking the CISS effect to the orbital Edelstein effect. In the latter, a drive current induces a finite orbital magnetization, even in the absence of spin-orbit coupling. Our non-equilibrium theory naturally explains key features of the CISS effect: its persistence in systems with weak or vanishingly small spin-orbit coupling and its connection to natural optical activity, a distinctive signature of chiral systems.

• The paper introduces an orbital Edelstein effect mechanism that drives nonlinear spin transport by inducing a current-dependent effective Zeeman field.
• It derives a generalized Fermi-Dirac distribution and spin-resolved conductivity in chiral conductors under finite drift conditions.
• The theory links chiro-optical responses to spin polarization, offering a predictive framework for chiral spintronics applications.

Theory of Nonlinear Spin Transport in Chiral Conductors: An Expert Summary

Context and Motivation

The chirality-induced spin selectivity (CISS) effect describes spin polarization of charge carriers in chiral, nonmagnetic systems under electrical bias. The effect challenges conventional spin transport theories, which typically require large spin-orbit coupling (SOC) or explicit magnetism. Extensive experimental evidence exists for strong CISS, notably in organic molecules with negligible intrinsic SOC, as well as in chiral inorganic crystals and self-assembled molecular systems. The exceptionally high polarization values observed at room temperature and their correlation with chiro-optical properties pose an open question regarding the microscopic mechanism behind CISS.

Existing theoretical approaches attribute CISS either (i) to SOC—standard or geometric—within the chiral structure or (ii) to spin-dependent interactions at molecule-substrate interfaces. Both mechanisms are insufficient to explain robust CISS in systems with weak or absent SOC and in substrate-free scenarios. The present paper proposes a framework resolving these issues by linking CISS to the orbital Edelstein effect (OEE), an orbital-magnetoelectric response manifesting in nonequilibrium conditions even in SOC-free systems.

Theoretical Framework

The central construct is a non-equilibrium, current-carrying state in a chiral conductor, achieved by an external electric field strong enough to drive quasi-stationary electron drift without full momentum relaxation. In this regime, strong electron-electron scattering produces a drifting Fermi distribution while the system remains homogeneous and time-independent on relevant experimental timescales.

Crucially, the authors show that in a chiral conductor, the drift current $\mathbf{j}_{\rm d}$ induces a net orbital magnetization $\mathbf{M}$, with the proportionality described by the longitudinal OEE response tensor $\chi^{\rm OE}_{\rm L}$. The induced orbital magnetization, even without explicit SOC, acts as an effective internal Zeeman field $B_{\rm eff} \parallel \mathbf{j}_{\rm d}$, thereby creating a spin splitting for the electrons. The result is a current-induced, Zeeman-like spin polarization of the charge carriers.

The theory yields a generalized Fermi-Dirac distribution, incorporating both momentum-shift (drift) and the energy splitting determined by the drift-induced $B_{\rm eff}$, parameterized to respect the handedness $\zeta$ of the chiral system. Analytical expansion for small drift reveals explicit forms for spin-resolved conductivity and spin polarization.

Nonlinear Spin Transport and Spin Polarization

The framework rigorously shows that, in the absence of a drift current (and thus in linear equilibrium), Onsager-Büttiker reciprocity forbids any measurable spin polarization in two-terminal devices. Only when operating in the nonlinear regime—i.e., with finite drift—do the leading-order corrections to the conductivity become spin-dependent and odd under reversal of molecular chirality. Specifically, the longitudinal spin polarization $\mathcal{P}_\parallel$ is nonlinear in the applied field and dominated by terms proportional to both the drift and the OEE coefficient.

Most notably, the theory robustly predicts that the magnitude and sign of the CISS effect are directly controlled by the OEE, and thus by chirality, independent of bare SOC. The spin polarization takes the form

$$\mathcal{P}_\parallel = \zeta\frac{\delta\mathcal{K}^{\rm A}_{\rm L} E}{\sigma^{(0)}/\mu_c + \delta\mathcal{K}^{\rm S}_{\rm L} E}$$

demonstrating the explicit nonlinear dependence and chiral control. For positive OEE and chirality, the polarization can attain values in line with those observed experimentally, even with weak SOC.

Connection to Chiro-optical Responses

A significant outcome is the established proportionality between the OEE and the magnetoelectric tensor responsible for natural optical activity (NOA). Utilizing thermodynamic and magnetoelectric arguments, the paper relates the linear OEE response to the imaginary off-diagonal dielectric response responsible for NOA in chiral materials. Hence, the CISS strength is not only symmetry-protected, but inherently tied to optical rotation (gyrotropy), both governed by the same microscopic mechanisms.

Implications and Perspectives

The presented framework provides a SOC-independent, orbital-magnetoelectric mechanism for CISS, capturing the main experimental phenomenology:

• Persistence of large CISS polarization in weak-SOC systems
• Nonlinear voltage dependence
• Proportionality between CISS and chiro-optical response
• Handedness-controlled spin selectivity

This theory unifies the explanation of CISS with known orbital responses in chiral materials and allows systematic analysis of additional factors such as electron correlation, quantum geometry, and phononic effects. It encompasses both transport and photoinduced excitation set-ups. Importantly, it can be explicitly parameterized using microscopic band structure and OEE, bridging ab initio calculations and spin transport measurements.

The analysis also highlights recent experimental findings of polarization in the nominal linear regime, suggesting possible new departures from the standard Onsager-Büttiker paradigm due to strong interactions or other emergent mechanisms.

Conclusion

The paper introduces a symmetry-grounded, orbital-magnetoelectric theory of CISS in chiral conductors, demonstrating that nonlinear spin transport and robust spin polarization can arise from non-equilibrium OEE, independent of intrinsic SOC. The direct proportionality to chiro-optical response provides both a predictive and diagnostic tool for characterizing spin-transport phenomena in chiral systems, suggesting new directions in chiral spintronics and functional materials discovery. The formalism enables future investigations into the interplay between orbital, spin, and optical phenomena—particularly the role of electron interactions and quantum geometry—in both transport and optoelectronic applications (2606.19274).