Enantiosensitive molecular compass

TL;DR

This work identifies a universal, dipole-only mechanism for chirality-induced spin selectivity (CISS) in spin-resolved photoionization of randomly oriented chiral molecules under isotropic illumination. It formulates a uniaxial spin–orientation coupling described by $G_{ij}$, recast as $G_{ij} = \kappa[\mathcal S_i \mathcal S_j + \gamma(|\mathcal S|^2 \delta_{ij}-\mathcal S_i \mathcal S_j)]$, with a Bloch molecular compass $\boldsymbol{\vec{S}}^{M}$ that governs enantioselective spin–orientation locking even after orientational averaging. The authors validate the framework with a synthetic chiral argon model, showing substantial locking of photoelectron spin to molecular geometry and demonstrating significant enhancements when using linearly polarized light through an additional vector $\boldsymbol{\vec{S}}'^{M}$, yielding up to ≈73% lock in certain geometries. By connecting orientation-conditioned spin polarization to orientation-conditioned CISS, the work unambiguously links the origin of CISS in photoionization to chiral spin–orbit–electric-dipole couplings and provides a route to identifying and exploiting spin–chirality correlations in broader chiral materials.

Abstract

Chirality describes the asymmetry between an object and its mirror image and manifests itself in diverse functionalities across all scales of matter - from molecules and aggregates to thin films and bulk chiral materials. A particularly intriguing example is chirality-induced spin selectivity (CISS), where chiral structures orient electron spins enantio-sensitively. Despite extensive research, the fundamental origin of spin-chirality coupling, the unexpectedly large magnitude of the CISS effect, and the possible role of electromagnetic fields in it remain unclear. Here, we address these issues by examining the simplest scenario: spin-resolved photoionization of randomly oriented chiral molecules. We uncover a universal mechanism of spin-selective chiral photodynamics, arising solely from electric-dipole interactions and previously unrecognized. This mechanism embodies a chiral molecular compass - a photoinduced magnetization vector that orients the photoelectron spin. It arises in photoexcited chiral molecules even under isotropic illumination, operates even in isotropic chiral media, and enables a phenomenon central to CISS: locking of the photoelectron spin orientation to molecular geometry. It shows that chiral molecules can sustain time-odd correlations whereas achiral molecules cannot. Our findings have broad implications, from unambiguously identifying the origin of CISS effect in photoionization to harvesting correlations underlying this effect in other forms of CISS in various chiral materials.

Figures (8)

• Figure 1: Spin-chirality coupling in photoionization of randomly oriented molecules under isotropic illumination is unique to chiral media. (a) The Bloch vector $\boldsymbol{\vec{S}}^M$ is "attached" to the molecule and represents the direction of molecular compass in chiral molecules . (b) After photoionization the cation cloud (grey) correlated to photoelectrons with specific spin projection on the spin detection axis $\boldsymbol{\hat{s}}^L$ possesses a net orientation such that $\boldsymbol{\vec{S}}^L$ is parallel to $\boldsymbol{\hat{s}}^L$. (c) The direction of spin to cation orientation locking is enantio-sensitive: the photoelectron spin is parallel (antiparallel) to $\boldsymbol{\vec{S}}^L$ for right (left) molecules. (d) The density matrix $\rho$ of a degenerate two-level system corresponding to spin-up $|\uparrow\rangle$ and spin-down $|\downarrow\rangle$ states of the photoelectron with energy $E=\frac{k^2}{2}$ can be averaged over molecular orientations to yield reduced density matrix $\varrho$. The Bloch vector $\boldsymbol{\vec{S}}^M$ is defined on the Bloch sphere in the molecular frame $\{\boldsymbol{\hat{\xi}}^M, \boldsymbol{\hat{\eta}}^M, \boldsymbol{\hat{\zeta}}^M\}$, and is proportional to the expectation value of the spin operator for a state with density matrix $\varrho$.
• Figure 2: Connection between spin-orientation locking and CISS. Both effects are enabled by the spin-orientation correlations described by the tensor $\mathbf{G}$ but they correspond to different measurements. (a) Spin-orientation locking is spin-conditioned measurement of an averaged orientation of randomly oriented ensemble upon ionization. Spin conditioning means that orientation is measured for the cations correlated to a given spin projection on the chosen detection axis. (b) CISS in photoionization is an orientation-conditioned measurement of an averaged spin. Orientation conditioning means that molecules contributing to the measurement must be oriented along a specific chosen axis (so-called one dimensional orientation) prior to photoionization.
• Figure 3: Comparison of the (a) isosurface and (b) contour plots of the chiral electronic states $| \psi_{-1,\frac{1}{2}}^{+}\rangle$ and $| \psi_{-1,\frac{1}{2}}^{-}\rangle$ shown in the top and bottom row (in the molecular frame), respectively, and colored according to its phase. The molecular $\{x,y,z\}$ axes are labeled as $\{\xi,\eta,\zeta\}$, respectively. The isosurface is set at $|\psi_{-1,\frac{1}{2}}^{\pm}|=3.2\times10^{-3} \text{Bohr}^{3/2}$. The contour plots are cuts on the $\xi=0$, $\zeta=0$, and $\eta=0$ planes. Thicker contour lines and darker shading correspond to higher values of the density. It can be seen that the probability density of the states $| \psi_{-1,\frac{1}{2}}^{\pm}\rangle$ are mirror images of each other.
• Figure 4: Enantio-sensitive spin-orientation locking under isotropic illumination of randomly oriented electronic states. (a) The Bloch pseudovector $\boldsymbol{\vec{S}}^M$ (internal directional bias) in the molecular frame for the chiral argon states. $\boldsymbol{\vec{S}}^M$ changes its direction in space as a function of the photoelectron momentum $k$. Trajectories traced by this vector are shown for $0<k<0.8 \text{ Bohr}^{-1}$. (b) Degree of orientation for chiral states with $m=1$, $\mu=\pm\frac{1}{2}$ (violet and orange correspondingly), and averaged over spin orientation in initial state (black). (c) Degree of orientation for chiral states with $m=-1$, $\mu=\pm\frac{1}{2}$ (red and green correspondingly) and averaged (black). The rapidly oscillating behavior at higher values of $k$ are due to the Fano resonances, leading up to the ionization threshold for the 3s electrons Samson2002Carlstroem2024spinpolspectral.
• Figure 5: Enantio-sensitive spin-orientation locking resulting from illumination of randomly oriented electronic states by linearly polarised fields in (a) orthogonal detection geometry $\boldsymbol{\hat{s}}^L\perp\boldsymbol{\hat{\epsilon}}^L$ [Eq. \ref{['eq:enhancement']}] and (b) collinear detection geometry $\boldsymbol{\hat{s}}^L\parallel\boldsymbol{\hat{\epsilon}}^L$ [Eq. \ref{['eq:reduction']}]. For both panels, $m=1$, $\mu=\pm\frac{1}{2}$ (violet and orange correspondingly), $m=-1$, $\mu=\pm\frac{1}{2}$ (red and green correspondingly) and black corresponds to spin unpolarised initial state.