Should it really be that hard to model the chirality induced spin selectivity effect?

TL;DR

The paper argues that the chirality induced spin selectivity (CISS) effect cannot be captured by independent-electron theories and requires explicit electron-electron interactions and environment coupling. It presents a minimal open-system model where electron-vibration coupling and reservoir damping generate a spin-density-wave–like molecular state, yielding a nonzero spin density $\langle\mathbf{s}_1\rangle \neq 0$ and a magneto-resistance that depends on reservoir magnetization, thereby signaling effective breaking of time-reversal symmetry and Onsager reciprocity in a non-equilibrium setting. The analysis emphasizes the crucial roles of boundary conditions and dissipation, showing that CISS signatures emerge only when the molecule is embedded in a macroscopic environment. The work points to non-adiabatic, Berry-force corrections and explicit reactant–catalyst electron-transfer models as promising avenues to connect these microscopic mechanisms to chemical reactivity, such as oxygen reduction/evolution reactions, and to guide future ab initio developments. Specifically, the magneto-resistance is often analyzed through the polarization metric $P = [J(M>0)-J(M<0)]/[J(M>0)+J(M<0)]$, illustrating how spin-dependent transport couples to measurable currents in open systems.

Abstract

The chirality induced spin selectivity effect remains a challenge to capture with theoretical modeling. While at least a decade was spent on independent electron models, which completely fail to reproduce the experimental results, the lesson to be drawn out of these efforts is that a correct modeling of the effect has to include interactions among the electrons. In the discussion of the phenomenon ones inevitably encounters the Onsager reciprocity and time-reversal symmetry, and questions whether the observations violate these fundamental concepts, or whether we have not been able to identify what it is that make those concepts redundant in this context. The experimental fact is that electrons spin-polarize by one or another reason, when traversing chiral molecules. The set-ups are simple enough to enable effective modeling, however, overcoming the grand failures of the theoretical efforts, thus far, and formulating a theory which is founded on microscopic modeling appears to be a challenge. A discussion of the importance of electron correlations is outlined, pointing to possible spontaneous breaking of time-reversal symmetry and Onsager reciprocity.

Figures (4)

• Figure 1: Schematics of the typical experimental set-ups. (a) In the photo-emission spectroscopy (PES), the molecule is adsorbed on a metallic substrate which is illuminated with linearly or circularly polarized light. The accelerated electrons are emitted from the loose end of the molecule and their spin-polarization is subsequently detected through Mott scattering. This procedure gives a direct measurement of the spin-polarization of the emitted electrons, hence, the spin selectivity generated in the molecule. (b) The transport experiments are conducted by measuring the charge current flowing through the molecule mounted between metallic leads, one of which is ferromagnetic. The chirality induced spin selectivity effect is measured indirectly as the response of the charge current to the magnetization of the ferromagnet. Here, the CISS magneto-resistance is used as the measure of spin selectivity.
• Figure 2: Reductionists view of the CISS magneto-resistance. (a), (b) Effective models of the transport set-ups with a ferromagnetic left reservoir and non-magnetic right. The potential barrier between the reservoirs are apparently of different heights, consequently leading to different currents (c) as functions of the voltage bias.
• Figure 3: Calculated electronic properties of chiral molecule reservoir heterostructure. Panels (a)--(h) display the site resolved densities for various situations, where (a)--(d) are with non-magnetic and (e)--(h) for ferromagnetic left reservoir. (a) Charge densities $n_{m\uparrow}+n_{m\downarrow}$ and (b) corresponding spin densities $n_{m\uparrow}-n_{m\downarrow}$ for (blue) $L$ and (red) $D$ enantiomer. (c), (d) Corresponding spin resolved charge densities for (c) $L$ and (d) $D$ enantiomers showing (blue) $n_{m\uparrow}$ and (red) $n_{m\downarrow}$. (e) Charge densities for the $D$-enantiomer for a ferromagnet left reservoir with spin-polarization (blue) ${\bf p}_L=0.2\hat{\bf z}$ and (red) ${\bf p}_L=-0.2\hat{\bf z}$. The vertical lines indicate the positions of the charge center-of-mass. (f) Difference between the charge densities $n_m=n_{m\uparrow}+n_{m\downarrow}$ in panel (e). (g), (h) Spin resolved charge densities for (g) ${\bf p}_L=0.2\hat{\bf z}$ and (h) ${\bf p}_=-0.2\hat{\bf z}$. (i) Charge current for (blue) ${\bf p}_L=0.2\hat{\bf z}$ and (red) ${\bf p}_=-0.2\hat{\bf z}$, (j) corresponding spin-polarizations $J_\uparrow-J_\downarrow$, and (k) normalized CISS magneto-resistance for ferromagnetic (blue) left and (red) right reservoir. (l) Schematics of the chiral molecule mounted in the junction between a (top, bottom) ferromagnetic and (middle) non-magnetic reservoir to the left and non-magnetic to the right. The calculations are made for helices with $3\times6$ sites, using $\lambda_0=1/50$, $t_\nu=1/20$ and $\lambda_\nu=1/500$ for a single $\nu$, $\Gamma_0=1$, $\varepsilon_{m}-\mu_0=-10$, $\omega_\nu=1/50$, and $\Phi=3/500$ in units of $t_0=0.1$ eV, calculated for $T=300$ K.
• Figure 4: Schematic of the oxygen reduction reaction catalyzed using chiral molecules. By spin selectivity, the chiral molecules provide triplet-like electron pairs with the same spin which neutralizes the angular momentum mismatch between the triplet state O$_2$ and singlet state end products.