Spin polarized enantio-sensitive multipolar photoelectron currents

Abstract

Photoelectron circular dichroism (PECD) manifests as a forward-backward asymmetry of electron emission in the direction orthogonal to the light polarization plane via one-photon ionization of chiral molecules with circularly polarized light. Multi-polar `PECD' currents, i.e., currents resolved along multiple directions, have also been predicted using two mutually-orthogonal linearly polarized light with carrier frequencies $ω$ and $2ω$. These currents arise from the interference between the one- and two-photon transitions. Here, we will show that photoelectron spin detection already reveals enantio-sensitive multi-polar currents in the one-photon regime since the two axes can be marked by the photoelectron momentum $\unitvec{k}$ and spin-detection axis $\unitvec{s}$. Specifically, we consider one-photon ionization of an isotropic ensemble of randomly oriented chiral molecules and show that the direction of the resulting photoelectron current is enantio-sensitively `locked' to the photoelectron's spin, which is mediated by two mechanisms. First, is the Bloch pseudovector which enables a collinear locking forming either a spin-sink or source for opposite enantiomers. Second, is the spin torque pseudovector that enables orthogonal locking forming a spin vortex in the polarization plane that rotates in opposite directions for opposite enantiomers. The former effect is a spin analog of photoelectron vortex dichroism (\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.129.233201}{Phys. Rev. Lett. \textbf{129}, 233201, 2022}) wherein the detected photoelectron spin encodes molecular chirality while the latter is reminiscent of the Rashba effect in solids

Figures (4)

• Figure 1: Specification of coordinates in the laboratory frame. The light field propagates along $\boldsymbol{\hat{z}}$. The unit vector $\boldsymbol{\hat{\epsilon}}$ is the polarization direction for linearly polarized light, while $\boldsymbol{\hat{\Xi}}$ is the direction of photon spin for circularly polarized light. Upon ionization, the photoelectron is ejected in the direction of $\boldsymbol{\hat{k}}$ with its spin measured parallel to $\boldsymbol{\hat{s}}$.
• Figure 2: Schematic of the resulting photoelectron currents for (a,b) linearly, and (c-f) circularly polarized light in the laboratory frame. The solid and dashed blue vectors denote the opposite directions of spin for opposite enantiomers. (a-d) The currents $\boldsymbol{\vec{j}}_{\text{lin}}$ and $\boldsymbol{\vec{j}}_r$ are enabled by the Bloch vector $\boldsymbol{\vec{\mathcal{S}}}_{\boldsymbol{\vec{k}}}$ which results to a collinear locking of the photoelectron current and spin $\boldsymbol{\vec{j}}\parallel\boldsymbol{\hat{s}}$. (e-f) The currents $\boldsymbol{\vec{j}}_{\text{PECD}}$ and $\boldsymbol{\vec{j}}_\tau$ are enabled by the spin-resolved propensity field $\vec{\mathbb{B}}_{\boldsymbol{\vec{k}}}$. The PECD current is not spin-sensitive, while $\boldsymbol{\vec{j}}_\tau$ presents a three-way orthogonal locking of the photoelectron current and spin with the photon spin.
• Figure 3: Comparison of the photoelectron currents enabled by the Bloch vector $\boldsymbol{\vec{\mathcal{S}}}_{\boldsymbol{\vec{k}}}$ for different chiral states [Eqs. \ref{['eq:p_state']}-\ref{['eq:c_state']}] via random illumination, linearly (a,b) and circularly polarized light (c,d) with either orthogonal or collinear detection geometry [see Fig. \ref{['fig:setup']}]. 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 4: (a,b) Comparison of the components of $\boldsymbol{\vec{j}}_{\text{circ}}$ for different chiral states [Eqs. \ref{['eq:p_state']}-\ref{['eq:c_state']}] with $\boldsymbol{\hat{s}}\parallel\boldsymbol{\hat{y}}$.