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arxiv: 2509.17817 · v1 · submitted 2025-09-22 · ❄️ cond-mat.mes-hall · cond-mat.str-el

Breaking of Time-Reversal Symmetry and Onsager Reciprocity in Chiral Molecule Interfacd with an Environment

J. Fransson This is my paper

Pith reviewed 2026-05-18 14:35 UTC · model grok-4.3

classification ❄️ cond-mat.mes-hall cond-mat.str-el
keywords chiral moleculesOnsager reciprocityspin selectivitytime-reversal symmetryspin-orbit couplingdissipative couplingclosed shell
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0 comments X

The pith

Coupling a chiral molecule to an electron reservoir locks its spin to its handedness and breaks Onsager reciprocity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

A chiral molecule normally forms a closed-shell spin-singlet state with zero net spin. When it couples to an electron reservoir, the dissipative interaction broadens the molecular energy levels and opens the closed shell. Molecular spin-orbit coupling then splits the levels in a way that depends on the molecule's chirality, stabilizing one spin configuration over the other. The resulting charge distribution on the molecule varies linearly with the reservoir magnetization, so no linear-response regime appears and Onsager reciprocity is violated. This supplies a direct theoretical account for the chirality-induced spin selectivity effect.

Core claim

The spin-configuration of a chiral molecule is enantiospecifically locked when coupled to an electron reservoir. The coupling opens up the molecular closed shell structure, which broadens the energy levels. Together with the molecular spin-orbit coupling, this dissipative coupling generates an effective spin-splitting of the molecular energy levels and facilitates stabilization of a chirality determined spin-configuration. Simultaneously, the molecular charge distribution is shown to depend linearly on the magnetization of the reservoir such that no linear response regime is established with respect to the external magnetization. Accordingly, the Onsager reciprocity theorem does not apply to

What carries the argument

Dissipative coupling to the reservoir combined with molecular spin-orbit coupling, which opens the closed shell and produces an effective chirality-determined spin splitting.

If this is right

  • The molecular spin configuration becomes fixed by the handedness of the molecule.
  • Molecular charge varies linearly with reservoir magnetization, eliminating the linear-response regime.
  • Onsager reciprocity fails to hold for the chiral molecule-reservoir system.
  • The mechanism accounts for chirality-induced spin selectivity without external magnetic fields.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Spin selectivity could appear in any chiral system whose levels are broadened by environmental coupling, even in mean-field models.
  • The same reciprocity breaking may occur in other dissipative chiral setups such as helical polymers or surfaces.
  • Device concepts could exploit molecular handedness alone to filter spin currents at interfaces.

Load-bearing premise

The dissipative coupling to the reservoir together with molecular spin-orbit coupling is sufficient to open the closed-shell structure and produce a stable, chirality-determined spin configuration without requiring additional external fields or explicit many-body correlations beyond mean-field treatment.

What would settle it

Direct measurement of a linear dependence between molecular charge and reservoir magnetization for a chiral molecule, or the disappearance of spin selectivity when the molecule is decoupled from any reservoir.

Figures

Figures reproduced from arXiv: 2509.17817 by J. Fransson.

Figure 1
Figure 1. Figure 1: FIG. 1. Curvature vector [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Site resolved (a) charge and (b) spin distributions for helical [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Site resolved charge distribution for a helical 3 [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. (a) Charge currents for a 3 [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. (a) Charge currents with (blue) [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. (a), (b) Site resolved non-equilibrium charge distributions [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Molecular closed shell structures are known to form spin-singlet configurations, resulting from the spin-exchange associated with electron-electron interactions. While the vanishing total spin-moment is an immanent property of the spin-singlet, the vanishing local moments is a result of fluctuations between degenerate spin-configurations. Here, it is demonstrated that the spin-configuration of a chiral molecule is enantiospecifically locked when coupled to an electron reservoir. The coupling opens up the molecular closed shell structure, which broadens the energy levels. Together with the molecular spin-orbit coupling, this dissipative coupling generates an effective spin-splitting of the molecular energy levels and facilitates stabilization of a chirality determined spin-configuration. Simultaneously, the charge molecular charge distribution is shown to depend linearly on the magnetization of the reservoir such that no linear response regime is established with respect to the external magnetization. Accordingly, the Onsager reciprocity theorem does not apply to a chiral molecule attached to a reservoir, hence, providing a theoretical foundation for the chirality induced spin selectivity effect.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that coupling a chiral molecule to an electron reservoir opens its closed-shell structure via dissipative broadening of energy levels. Combined with molecular spin-orbit coupling, this generates an effective spin-splitting that stabilizes a chirality-determined spin configuration. The molecular charge distribution depends linearly on the reservoir magnetization, implying no linear response regime and thus the inapplicability of the Onsager reciprocity theorem, providing a theoretical foundation for the chirality-induced spin selectivity effect.

Significance. If the result holds, this analytic derivation would supply a mechanism for CISS based on dissipative coupling and SOC without external fields, with the explicit construction of effective spin splitting from the product of spin-orbit strength and dissipative broadening as a clear strength. The significance is reduced by the absence of bounds ensuring mean-field stability, limiting direct applicability to real closed-shell organics.

major comments (2)
  1. [Model construction and effective spin-splitting derivation] The stabilization of the chirality-locked spin configuration is achieved by opening the closed shell through dissipative reservoir coupling (broadening Gamma) followed by molecular SOC (strength lambda) to produce an effective spin-splitting. This step implicitly employs a mean-field treatment of the resulting open-shell state. No explicit bounds are derived on the electron-electron interaction U relative to Gamma or temperature to ensure the polarized state survives quantum fluctuations between near-degenerate configurations, which is load-bearing for the central claim of a stable, chirality-determined spin configuration.
  2. [Onsager reciprocity and linear response discussion] The assertion that Onsager reciprocity does not apply is based on the linear dependence of molecular charge distribution on reservoir magnetization. This dependence is generated within the model by the product of the dissipative broadening Gamma and SOC strength lambda, both introduced as free parameters without independent fixing by external data, so the predicted spin polarization remains tied to these input choices.
minor comments (2)
  1. [Abstract] The abstract refers to 'molecular charge distribution' without specifying the precise observable (e.g., total charge or dipole); adding this would improve clarity.
  2. [Throughout the manuscript] Notation for the effective spin-splitting could be assigned an equation number to facilitate cross-referencing in the derivation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments. We address each major comment below, providing clarifications on the model and indicating where revisions will be made to strengthen the presentation.

read point-by-point responses

  1. Referee: [Model construction and effective spin-splitting derivation] The stabilization of the chirality-locked spin configuration is achieved by opening the closed shell through dissipative reservoir coupling (broadening Gamma) followed by molecular SOC (strength lambda) to produce an effective spin-splitting. This step implicitly employs a mean-field treatment of the resulting open-shell state. No explicit bounds are derived on the electron-electron interaction U relative to Gamma or temperature to ensure the polarized state survives quantum fluctuations between near-degenerate configurations, which is load-bearing for the central claim of a stable, chirality-determined spin configuration.

    Authors: We acknowledge that the effective description of the stabilized spin configuration involves an approximation that can be viewed as mean-field for the open-shell state created by reservoir coupling. The effective spin splitting arises explicitly from the product of the dissipative broadening Gamma and the SOC strength lambda, which lifts the degeneracy between spin configurations and selects the chirality-determined one. While the current derivation does not include explicit quantitative bounds on U relative to Gamma or temperature, the stabilization mechanism relies on Gamma being sufficient to suppress fluctuations between near-degenerate states. In the revised manuscript we will add a dedicated paragraph in the discussion section outlining the regime of validity. This will include the qualitative condition that Gamma should exceed the scale of residual exchange or thermal fluctuations for the polarized state to remain stable, together with order-of-magnitude estimates drawn from typical molecular parameters (Gamma ~ 0.1–1 eV in chemisorbed systems). A full many-body treatment deriving rigorous bounds lies beyond the present effective-model scope but is noted as a natural direction for follow-up work. revision: partial

  2. Referee: [Onsager reciprocity and linear response discussion] The assertion that Onsager reciprocity does not apply is based on the linear dependence of molecular charge distribution on reservoir magnetization. This dependence is generated within the model by the product of the dissipative broadening Gamma and SOC strength lambda, both introduced as free parameters without independent fixing by external data, so the predicted spin polarization remains tied to these input choices.

    Authors: The linear dependence of the molecular charge distribution on reservoir magnetization is a direct consequence of the model and is generated by the product Gamma × lambda. This linearity implies that the system lacks a conventional linear-response regime with respect to an external magnetization, thereby placing the setup outside the domain where Onsager reciprocity is required to hold. Gamma and lambda are indeed input parameters, but they carry clear physical meaning: lambda is the intrinsic molecular spin-orbit coupling (computable from first principles), and Gamma is the level broadening set by the molecule–reservoir coupling strength (experimentally tunable via interface engineering). The central theoretical result—that reciprocity is violated for any nonzero values of these parameters—does not depend on their specific numerical values. In the revision we will expand the relevant section to clarify this point and to indicate how the parameters can be constrained independently, for example by matching to ab-initio calculations of SOC or by fitting to measured interface conductances. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is model-based and self-contained

full rationale

The paper introduces a theoretical model in which dissipative reservoir coupling broadens molecular levels and, combined with spin-orbit coupling, produces an effective spin splitting that locks a chirality-determined configuration. The subsequent demonstration that molecular charge distribution depends linearly on reservoir magnetization (thereby violating the linear-response assumption underlying Onsager reciprocity) is obtained directly from the model's equations rather than by re-labeling an input or by self-citation reduction. No fitted parameters are presented as independent predictions, and the central claim does not collapse to a definitional identity or an unverified self-citation chain. The construction is therefore independent of its own outputs.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on a mean-field treatment of an open molecule whose spin configuration is stabilized by the product of spin-orbit coupling and reservoir-induced level broadening; no independent experimental anchor for the broadening parameter is supplied.

free parameters (2)
  • dissipative broadening Gamma
    Introduced to open the closed-shell structure; its magnitude controls the size of the effective spin splitting.
  • molecular spin-orbit strength lambda
    Standard parameter whose value is not fixed by the present derivation.
axioms (1)
  • domain assumption The molecule-reservoir coupling can be treated within a non-equilibrium Green's function or rate-equation framework that preserves the chirality dependence of the spin-orbit term.
    Invoked to generate the effective spin splitting from the product of Gamma and lambda.

pith-pipeline@v0.9.0 · 5712 in / 1397 out tokens · 35873 ms · 2026-05-18T14:35:28.256372+00:00 · methodology

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Reference graph

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