Theory of CISS: Progress and Challenges (Evers, Kronik et al., 2021)

"Theory of Chirality Induced Spin Selectivity: Progress and Challenges" was posted to arXiv (2108.09998) on 23 August 2021. Its 22 authors, with Ferdinand Evers (University of Regensburg) first and Leeor Kronik (Weizmann Institute of Science) last, are theorists and experimentalists who took part in a workshop hosted by the Weizmann Institute of Science in early 2020, and the paper grew out of those discussions. They include Ron Naaman, who co-authored, with Ray, Ananthavel and Waldeck, the 1999 Science study that the review credits as the first transmission experiment. It is useful to this dossier because it is a joint critical overview by theorists and experimentalists working on Chirality-Induced Spin Selectivity (CISS) that sets out what theory cannot yet explain, and it states plainly where the authors see no consensus.

What the review says CISS is

For the authors, CISS is an umbrella label for a whole family of observations rather than one effect. What links them is that a molecule's handedness, left versus right, influences which spin direction electrons favour. In practice that shows up in three kinds of experiment:

• Electrons fired into vacuum. Light frees electrons from a metal surface coated with chiral molecules, and the experiment checks whether those that make it through the coating favour one spin. This is the oldest kind; the review traces it to Ray et al. (Science, 1999).
• Electrons in a circuit. A chiral film or molecule sits between electrical contacts, often with one magnetic contact, and the current changes depending on which way that magnet points. The review says this is where most of the work so far has been done.
• Chemistry. Electron spin is used to treat left- and right-handed versions of a molecule differently, for example in reactions or in adsorption onto a magnetised surface. This is the newest kind.

The experimental record as the review summarises it

The survey quotes several headline figures. Göhler et al. used a Mott polarimeter on photoelectrons passing through a monolayer of 78-base-pair double-stranded DNA on gold. They found polarisations of roughly −55% to −61%, even when the light was linearly polarised. Heptahelicene contains only carbon and hydrogen and has a single helical turn, yet it is reported to give about 6% to 8% longitudinal polarisation. Among transport results, the authors list up to 80% spin selectivity in polyaniline micro-fibres 2–6 µm long at room temperature, and more than 85% in coronene bisimide and porphyrin-based materials. Chiral perovskites gave up to 86% with methylbenzylammonium lead iodide and up to 94% with the tin-iodide analogue.

On the chemistry side, the review describes spin-selective anodes that are said to boost water splitting while reducing hydrogen peroxide formation. It also covers separation of enantiomers by adsorption on magnetised cobalt/gold substrates, and a report that chiral monolayers alone reversed the magnetisation of a thin ferromagnet.

The authors attach a caveat to all of this. Debate over the measurements continues, CISS is "not always observed in transport through chiral media", and nobody agrees yet on the exact conditions under which a given form of the effect should appear. They also note two patterns: CISS tends to track optical activity, and it shows up most clearly in the non-linear current-voltage regime.

The magnitude problem

This is the central issue of the review. Spin-orbit coupling (SOC) is the obvious candidate mechanism, because it links an electron's motion to its spin. The review notes that a simple classical estimate, treating the electron as current flowing around a helical path, gives an effect many orders of magnitude too small. More careful SOC calculations reproduce the effect qualitatively, but they have consistently predicted polarisations up to several orders of magnitude below the measured values.

The review applies the same test to every proposal it surveys:

• Scattering models for transmission show qualitatively that SOC polarises spin, but give polarisations far too small for realistic parameters. Gersten et al. added the substrate's own SOC, but the authors say there is no consensus that this closes the gap. CISS has also been seen on substrates whose SOC is negligible.
• First-principles DNA calculations by Maslyuk et al. found stronger filtering in a helix than in a straightened strand. That fits with symmetry, but the result was about an order of magnitude below experiment. Rebergen and Thijssen reached the same conclusion.
• Tight-binding models are the basis of many of the studies surveyed. In an early example, Gutierrez et al. used a single-channel model and reported spin polarisation reaching up to 100% near the band edges. The review points out that this depends on the parameters chosen: a hopping parameter of 20–40 meV, motivated by DNA, and an SOC of about 2 meV taken from a heuristic argument. The authors accept that light elements can reach meV-scale SOC in other settings, but argue that the symmetry breaking caused by chirality should be weaker by a geometric factor involving the helix's pitch and diameter.

Symmetry rules that limit any explanation

The review stresses two general constraints from spintronics:

1. In a wire with only one conduction channel, SOC can be removed mathematically by a gauge transformation. SOC alone therefore cannot filter spin there. The review notes that several earlier papers stressed the importance of two channels for this reason.
2. Even with several channels, an Onsager argument based on time-reversal symmetry rules out spin filtering in the linear (low-bias) regime of a two-terminal device. If the device filtered spin, its conductance would change when a magnetic analyser electrode was flipped. Reciprocity forbids that change.

According to the review, many published single-channel models nonetheless report chirality-selective spin transport. It says each such model should be checked against these limits, because some violations may reflect mistakes in the analysis. This is the same Nonreciprocity question taken up by Electrostatic Contact-Potential Mechanism for CISS Magnetoresistance.

Proposed ways around the limits

The authors catalogue the workarounds without endorsing any of them:

• Coupling to a third bath that causes dephasing or leakage, breaking time-reversal symmetry effectively. The resulting polarisation depends strongly on a leakage rate whose real size is unknown. In simulations that rate is typically a few percent of the hopping integral, which the authors say should also produce large resistance effects.
• Friction-based many-body models (Volosniev et al.). The review notes that the source of the friction and the energy supply it requires are not specified.
• Coupling to atomic nuclei, possibly strengthened near conical intersections.
• Non-equilibrium incoming electrons (Dalum and Hedegård), which suit photoemission better than ordinary conductance measurements.
• An orbital-polarisation model in which SOC in the electrodes converts orbital polarisation into spin polarisation (Liu et al.).
• A phenomenological transfer-matrix approach (Yang, van der Wal and van Wees). It finds no two-terminal linear-response signal but allows signals in non-linear and multi-terminal setups.
• A curved-space-time Dirac-equation approach. The review calls it conceptually appealing but limited by having only one parameter, the curvature of the helical path.

For the chemistry category, the authors say first-principles work shows that spin polarisation could explain enantioselectivity if chirality produces it. They add that no full framework yet explains how it does.

What the review does and does not establish

The paper reports no new measurements. Its conclusion is that no single microscopic CISS mechanism has been shown to account for all the experiments. CISS may be a family of phenomena united only by the interplay of SOC and chirality, and "a large gap remains" between observation and theoretical estimates. The authors call for more experiments on model systems and for theory on transient CISS signals, which steady-state models largely ignore. For the rest of this dossier, the review sets a clear baseline. Any mechanism paper, including the spinterface model discussed in The Spinterface Mechanism for CISS: A Critical Perspective, can be judged by whether it explains the measured magnitudes while respecting the gauge and Onsager constraints.

Reference

• F. Evers, A. Aharony, N. Bar-Gill, O. Entin-Wohlman, P. Hedegård, O. Hod, P. Jelinek, G. Kamieniarz, M. Lemeshko, K. Michaeli, V. Mujica, R. Naaman, Y. Paltiel, S. Refaely-Abramson, O. Tal, J. Thijssen, M. Thoss, J. M. van Ruitenbeek, L. Venkataraman, D. H. Waldeck, B. Yan and L. Kronik, "Theory of Chirality Induced Spin Selectivity: Progress and Challenges," arXiv:2108.09998v1 (23 August 2021).