Symmetry considerations in chirality-induced spin selectivity

arXiv:2610.01880 · cond-mat.mes-hall, physics.chem-ph, quant-ph · Submitted 2026-10-01 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: Today's paper: "Symmetry considerations in chirality-induced spin selectivity".

Mira: The gist: CISS does not violate any fundamental symmetries including parity and time-reversal, providing a robust conceptual foundation for interpreting experiments and guiding future theoretical and experimental designs.

Kai: First, who's behind it and why it matters.

Title and authors: Kai: So we're looking at this paper called "Symmetry considerations in chirality-induced spin selectivity." Mira and I were looking at the title and who wrote it. It sounds a bit heavy, like we're diving deep into the math behind something already messy.

Mira: Yeah, it really does sound theoretical. The authors are Budker and Wittmann from institutions in Germany and California; they’re bringing a particle physics background to this molecular effect that’s usually in chemistry or condensed matter. It makes you wonder how they connect those dots, doesn't it?

Kai: Exactly. When you see "Symmetry considerations," you expect some kind of fundamental physics underpinning the weird spin-selectivity stuff we see in molecules. It suggests they aren't just looking at the experiments but trying to explain *why* it happens using universal rules.

Lev: From a hardware standpoint, if they're talking about fundamental symmetries, that’s huge for us because it tells us what kind of experimental setups we need to be able to trust. If the underlying physics respects parity and time reversal, then our measurements should behave in a predictable way regardless of the setup.

Mira: Right. The implication here is that they are using these fundamental symmetry rules—parity and time reversal—as a framework to interpret all the different CISS effects we’ve seen so far, moving past just observing what happens to actually understanding the mechanism better.

The paper's summary: Kai: So, what’s the main point they are trying to make in this paper about "Symmetry considerations in chirality-induced spin selectivity"? Basically, it seems like they’re taking all those different CISS systems and using the language of symmetry to sort them out.

Mira: Right. The summary suggests that the core idea is showing that CISS doesn't actually violate any fundamental symmetries, specifically parity and time reversal, which has been a big point of debate in the field for a long time.

Kai: That’s what I heard. They are positioning these effects not as some weird anomaly, but as phenomena that can be described using the same language we use to talk about particle interactions. It's about anchoring CISS within that universal symmetry language to give us a solid foundation for interpreting experimental results.

Lev: If they can prove it respects these symmetries, it means we don’t need to throw out entire classes of theories just because the effect is strange; we can treat it as a predictable consequence of the established rules.

Mira: That’s the big conceptual move here. By showing that CISS doesn't break parity or time reversal, they are offering a robust way forward for both theory and future experimental designs. It gives us something solid to build on instead of just chasing the observed effects in isolation.

The paper's improvements: Kai: Now, the paper points out some specific ways this symmetry approach helps. It talks about using rotational invariants to study how different experimental parameters affect the effect, like reversing them.

Mira: Exactly. They introduce rotational invariants to track how things transform when you reverse experimental settings, which is a clever way to test the underlying structure of the phenomenon without relying on messy numerical simulations every time.

Kai: It seems they specifically point out that for dynamic CISS, they can use a specific rotational invariant like "chi s dot J," and this specific combination is P- and T-even, which describes the full phenomenology of dynamic CISS.

Lev: That's interesting for me because it gives us a concrete formula to test. If we have an experiment where we measure that specific invariant, we know immediately whether it fits the expected symmetry constraints before even looking at the raw data.

Mira: And they also discuss quasi-static CISS, where things get trickier because they introduce dissipation into the picture. They show that for those cases, you can build a rotational invariant like "i chi d dot m," but this one is T-odd, which seems to be where the confusion comes from.

Kai: So the improvement here is distinguishing between effects that are fundamentally symmetric and those that require considering dissipation to restore time reversal invariance. That’s a clear way to separate the fundamental physics from experimental conditions like friction or heat loss.

Conclusion: Mira: To wrap up, the authors of "Symmetry considerations in chirality-induced spin selectivity" are using these symmetry tools—parity and time reversal—to provide a conceptual framework for understanding CISS. They are showing that CISS doesn't violate those fundamental symmetries, which gives us a very strong foundation to interpret what we see in experiments and where to direct future theoretical work.

Kai: It’s about moving from just observing the spin selectivity to understanding the deep structural rules governing it, using these invariants as our guide. It helps clarify when dissipation is actually necessary for certain effects and when it isn't.

Lev: From an error correction viewpoint, being able to identify which processes are symmetry-preserving versus those that are fundamentally T-violating or require dissipation means we can design more realistic error correction protocols for any quantum system exhibiting CISS.

Mira: It’s a nice way to frame the entire field. We take a family of diverse experimental observations and unify them under the umbrella of fundamental physics principles, which is what we need to move forward in this area. That's it for this paper on "Symmetry considerations in chirality-induced spin selectivity."

Dmitry Budker, Angela Wittmann

Helmholtz-Institut Mainz · GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH

cond-mat.mes-hall, physics.chem-ph, quant-ph

Submitted: 2026-10-01

Updated: 2026-10-01

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 71/100

The gist: The gist: CISS does not violate any fundamental symmetries including parity and time-reversal, providing a robust conceptual foundation for interpreting experiments and guiding future theoretical and

Key concepts

Chirality as a Pseudoscalar
Chirality is defined as a pseudoscalar property ($\chi$) that changes sign when space is inverted (P) but stays the same under time reversal (T). This means it's a fundamental characteristic of a system, like randomly oriented screws, which can be chiral even if it has no preferred direction.
Parity and Time-Reversal Invariance
The paper focuses on discrete symmetries, specifically spatial inversion (P) and time reversal (T). It emphasizes that the CISS effects discussed do not break these fundamental laws of physics, which helps establish a robust conceptual foundation for interpreting experimental results.
Rotational Invariants
These are mathematical quantities used to study how CISS behaves when experimental parameters change. They help clarify whether an effect is P-even or T-odd, allowing researchers to determine the necessary conditions, such as the role of dissipation, required for time-reversal invariance.

Terminology

Summary

The gist: CISS does not violate any fundamental symmetries including parity and time-reversal, providing a robust conceptual foundation for interpreting experiments and guiding future theoretical and experimental designs.

Introduction to CISS

The chirality-induced spin selectivity (CISS) effect, which is the coupling between structural chirality and electron spin polarization, has been experimentally observed across many diverse systems <ref:2610.01880#pg6>. The effect offers a pathway to generating and controlling spin polarization via structural chirality <ref:2610.01880#pg4>. CISS is a family of fascinating phenomena that connect molecular chirality with electron spins, tracing earlier work from discussions on scattering crosssections on chiral molecules of electrons with opposite helicity <ref:2610.01880#pg3>. Scientists have vigorously debated the origin of the effect and theoretical models were unable to predict the CISS effects quantitatively for a long time <ref:2610.01880#pg5>.

Chirality as a Pseudoscalar

Chirality is characterized as a pseudoscalar property (χ) that changes sign upon spatial inversion (P) and remains invariant under time reversal (T) <ref:2610.01880#pg4>. An example of such a system is a collection of randomly oriented screws which is T-invariant and obviously chiral <ref:2610.01880#pg4>. While chirality is not necessarily associated with spin, it can be associated with an ensemble of spins, such as the correlation also known as rotational invariant ⃗s · ⃗p, where ⃗p is the linear momentum of the particle with spin <ref:2610.01880#pg4>.

Symmetry Properties

The paper focuses on discrete symmetries such as spatial inversion (P) and time reversal (T) <ref:2610.01880#pg5>. The authors emphasize that the effects discussed in this paper do not break any fundamental symmetries, specifically neither parity nor time reversal invariance <ref:2610.01880#pg5>. Rotational invariants are used to study the behavior of the effect under reversals of experimental parameters <ref:2610.01880#pg6>. For instance, in beta decay, the rotational invariant is T-even but P-odd, meaning it violates parity but preserves time-reversal invariance <ref:2610.01880#pg6>.

Dynamic CISS

The simplest dynamic CISS effect involves generating spin polarization when a charge current flows through a chiral molecule <ref:2610.01880#pg8>. This phenomenon can be represented by the rotational invariant: ⃗s·J⃗, which is T-even (as both ⃗s and J⃗ are T-odd) and P-odd (as ⃗s is P-even and J⃗ is P-odd) <ref:2610.01880#pg8>. The full correlation for dynamic CISS is written as the Rotational invariant for dynamic CISS: χ⃗s · J <ref:2610.01880#pg8>. This rotational invariant is P- and T-even and fully describes the phenomenology of dynamic CISS <ref:2610.01880#pg8>.

Quasi-Static CISS

In quasi-static CISS effects, the interaction of a chiral overlayer on a magnetic layer can influence the magnetization of the latter <ref:2610.01880#pg5>. A rotational invariant χ(⃗d · ⃗m) can be built for this interaction, which is P-even <ref:2610.01880#pg5>. However, this rotational invariant is also T-odd, while correlations that do not involve weak interactions are expected to be both P and T even <ref:2610.01880#pg5>. The final ingredient needed to resolve the conundrum and restore fundamental T-invariance is the realization of dissipation <ref:2610.01880#pg6>. This suggests that apparently T-odd correlations become allowed when dissipation is involved <ref:2610.01880#pg6>. For Ohm’s law, a rotational invariant can be defined as i⃗j · E⃗, which indicates that dissipation is at play in the process <ref:2610.01880#pg6>.

Conclusion and Outlook

The approach using rotational invariants illustrates how CISS effects do not violate any fundamental symmetries <ref:2610.01880#pg8>. This method helps clarify when dissipation plays an essential role in a particular effect and when it does not <ref:2610.01880#pg8>. The insights gained could lead to new research areas, such as employing the CISS effect to hyperpolarize atomic nuclei <ref:2610.01880#pg8>.

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Symmetry considerations in chirality-induced spin selectivity<ref:2610.01880#pg5>

Dmitry Budker∗

Helmholtz-Institut Mainz, 55128 Mainz, Germany

GSI Helmholtzzentrum f¨ur Schwerionenforschung GmbH, 64291 Darmstadt, Germany

QUANTUM, Institut f¨ur Physik, Johannes Gutenberg-Universit¨at, 55128, Mainz, Germany and

Department of Physics, University of California, 94720-7300 Berkeley USA

Angela Wittmann †

Institute of Physics Johannes Gutenberg-University Mainz 55128 Mainz Germany

Abstract

The chirality-induced spin selectivity (CISS) effect the coupling between structural chirality and electron spin polarization has been experimentally observed across many diverse systems; however, despite extensive theoretical effort, a unified mechanistic understanding remains elusive <ref:2610.01880#pg5>. In this perspective we demonstrate how some of the basic properties of the fascinating effects of CISS can be understood based on straightforward symmetry considerations commonly employed in fundamental particle physics <ref:2610.01880#pg5>. In particular we show that CISS does not violate any fundamental symmetries including parity and time-reversal <ref:2610.01880#pg5>. By anchoring CISS within the universal language of symmetry we offer a robust conceptual foundation for interpreting experiments and guiding future theoretical and experimental designs <ref:2610.01880#pg5>.

Dedicated to the memory of Prof. David Waldeck (1956-2026) and Prof. Vladimiro Mujica (1956-2026).

∗ budker@uni-mainz.de

† a.wittmann@uni-mainz.de

1

arXiv:2610.01880v1 [cond-mat.mes-hall] 1 Oct 2026

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I. INTRODUCTION

In summer of 2025 some 160 scientists from around the world including Professors David Waldeck and Vladimiro Mujica gathered for a week-long conference in New England to discuss the mechanisms and applications of the chirality-induced spin-selectivity (CISS) effect that has already left a profound mark on a remarkably diverse array of disciplines ranging from magnetism of layered magnetic materials to biology to magnetic resonance and even geophysics <ref:2610.01880#pg3>. Controlling electron spin a key quantum mechanical property using a macroscopic tool in the absence of magnetic field has been a longstanding challenge <ref:2610.01880#pg5>. The chirality-induced spin-selectivity effect offers a pathway to generating and controlling spin polarization via structural chirality <ref:2610.01880#pg5>.

The CISS effect first observed experimentally in 1999 [1] and further explored in a series of pioneering papers [2–8] is, in fact, a family of fascinating phenomena that connect molecular chirality with electron spins <ref:2610.01880#pg3>. As with many things in science one can trace earlier work anticipating CISS <ref:2610.01880#pg4>. For example Ref. [9] discussed the difference in scattering crosssections on chiral molecules of electrons with opposite helicity an effect similar to that of optical circular dichroism <ref:2610.01880#pg4>. The discussion was later extended to the effects in the interaction of unpolarized electrons and radiation with chiral molecules in the presence of magnetic field [10]. From the early days of CISS to today scientists have vigorously debated the origin of the effect and for a long time theoretical models were unable to predict the CISS effects quantitatively <ref:2610.01880#pg5>.

Of central importance to our discussion here is the concept of chirality which is a pseudoscalar property (χ) characterizing a physical system that changes sign upon spatial inversion (P) and remains invariant under time reversal (T) [12]. An example of such a system would be a collection of randomly oriented screws see Fig. 1a <ref:2610.01880#pg4>. Note that such a system does not have any preferred direction is T-invariant and obviously chiral it would rotate a probe particle such as a wooden ball propagating through the medium in a particular sense clockwise in the case of right-handed screws <ref:2610.01880#pg4>.

Improvements for AI systems

  1. The AI system can be designed to rigorously analyze experimental data related to chirality-induced spin selectivity (CISS) by constructing rotational invariants as described in Section III and IV. This allows the system to determine whether observed effects violate fundamental symmetries like parity or time-reversal, distinguishing between phenomena that are P- and T-even versus those that require dissipation, such as the distinction between dynamic CISS and quasi-static CISS effects.

  2. The AI can predict the expected behavior of CISS observables under parameter reversals by applying the principles of rotational invariants. Specifically, it can calculate how a quantity like the rotational invariant for dynamic CISS: χ⃗s · J⃗ transforms when the direction of the current and molecular chirality are reversed, providing a theoretical framework to interpret experimental results.

  3. The AI can differentiate between fundamental symmetry violations and dissipative effects in quasi-static CISS scenarios. It can determine whether an observed correlation, such as the one described by Rotational invariant for quasi-static CISS: iχ(⃗d · ⃗m), is indicative of fundamental T-violation or weak interactions or if it is instead a consequence of dissipation, which the paper suggests can alleviate this apparent T-violation.

Abstract

The chirality-induced spin selectivity (CISS) effect, the coupling between structural chirality and electron spin polarization, has been experimentally observed across many diverse systems. However, despite extensive theoretical effort, a unified mechanistic understanding remains elusive. In this perspective, we demonstrate how some of the basic properties of the fascinating effects of CISS can be understood based on straightforward symmetry considerations commonly employed in fundamental particle physics. In particular, we show that CISS does not violate any fundamental symmetries including parity and time-reversal. By anchoring CISS within the universal language of symmetry, we offer a robust conceptual foundation for interpreting experiments and guiding future theoretical and experimental designs.

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