Spin Dependence of Charge Dynamics and Group Velocity in Chiral Molecules

TL;DR

Using a tight-binding representation of a chiral molecule and time-dependent Landauer-Büttiker transport, the study computes spin-resolved occupancies $n_{m,\pm}(t)$ and local spin polarizations $p_m(t)$ to understand $CISS$ dynamics. It identifies a spin-dependent group-velocity asymmetry as the mechanism generating nonzero spin polarization, and shows that this polarization persists in a steady state when the molecule is coupled to two leads. The results qualitatively reproduce the magnetic-field trends observed in monolayer experiments on oligopeptides, and provide insight into how SOC and transport parameters shape spin polarization. The work also highlights potential current-induced magnetic-field effects in Hall measurements and suggests that molecular interactions could amplify spin signals.

Abstract

Chiral molecules are known to preferentially select electrons with a particular spin state, an effect termed chirality-induced spin selectivity (CISS). In this work, the transient CISS dynamics in a chiral molecule are investigated through time-dependent quantum-transport simulations, an important step toward further understanding CISS and its application in devices such as magnetoresistive random access memories and spin-based quantum computers. We show that a nonzero spin polarization throughout the chiral molecule can be attributed to a spin-dependent group velocity of electrons. Contrary to the case where a chiral molecule is connected to a single lead, this spin polarization persists into the steady state when two leads are connected. We show that the simulated spin polarization qualitatively agrees with a reference experiment, as evidenced by the distinct magnetic-field signatures calculated from the spin polarization within a monolayer of chiral molecules.

Figures (5)

• Figure 1: (a) Density and (d) spin polarization of electrons throughout a one-lead chiral molecule resulting from a transient calculation following application of a source potential $V_{\text{S}} = -0.5\;\text{V}$ at $t=0$. Markers $A$, $B$, and $C$ used in panels (a) and (d) are referenced by the main text. Electron density for (b) spin-$|+\rangle$ and (c) spin-$|-\rangle$ electrons, where group velocities are marked based on the density derivatives of site $1$ and $\mathbb{M}$ from the insets. To improve visibility, the colormaps of $n_m(t)$ and $n_{m,\pm}(t)$ were capped at 1.6 and 0.8, respectively. The average group velocity magnitude of spin-$|+\rangle$ and spin-$|-\rangle$ beams, denoted $v_{g,\text{ave}}$, and the difference in group velocity magnitudes of spin-$|+\rangle$ and spin-$|-\rangle$ beams, denoted $v_{g,\text{diff}}$, are shown as a function of (e) $\lambda_0$ and (f) $t_0$, where numerical results from transient calculations are compared to analytical results. Throughout, quantities related to $+\hat{\bm{z}}$- and $-\hat{\bm{z}}$-moving beams are indicated by green and cyan markers, respectively. All unvaried parameters were set according to Sec. \ref{['Sec::Parameters']}.
• Figure 2: (a) Density and (b) spin polarization of electrons throughout a two-lead chiral molecule resulting from a transient calculation following application of a source potential $V_{\text{S}} = -0.5\;\text{V}$ at $t=0$. To improve visibility, the colormap of $n_m(t)$ was capped at 1.4. Panel (b) inset shows the steady-state time constant $\tau_{\text{ss}}$ resulting from an exponential fit of the site-averaged spin polarization $\bar{p}(t)$, and the steady-state site-averaged spin polarization $\bar{p}_{\text{ss}}$. Characterization of $\bar{p}_{\text{ss}}$ as a function of (c) $E_{\text{S}}$ and $T$, (d) $\lambda_0$, and (e) $t_0$ and $\Gamma_0$. Characterization of $\tau_{\text{ss}}$ as a function of (d) $\lambda_0$ and (f) $t_0$ and $\Gamma_0$. All unvaried parameters were set according to Sec. \ref{['Sec::Parameters']}, except for panels (e) and (f), where $E_{\text{S}}$ was set sufficiently high to fill all conducting states.
• Figure 3: (a) Diagram (not to scale) of the reference experiment 2017_Kumar_ChiralityInducedSpinPolarizationPlacesSymmetry showing the magnetic field generated over a Hall sensor by a monolayer of chiral molecules when $V_{\text{G}}$ is applied. (b) Hall voltage for a monolayer of $X$-$($l-Ala-l-Aib$)_5$-$Y$ oligopeptides with $V_{\text{G}} = -10\;\text{V}$ applied at $t=0$, extracted from Ref. 2017_Kumar_ChiralityInducedSpinPolarizationPlacesSymmetry. (c) Peak Hall voltage for a variety of monolayers at various $V_{\text{G}}$, extracted from Ref. 2017_Kumar_ChiralityInducedSpinPolarizationPlacesSymmetry. Here, $X$-$($Ala-Aib$)_n$-$Y$ has $2n$ residues of chirality l or d, where $X=\text{SHCH2CH2CO}$ and $Y = \text{COOH}$. (d) Diagram (not to scale) of our monolayer model showing the magnetic field generated by chiral molecules when $V_{\text{S}}$ is applied at $t=0$. (e) Magnetic field from the spin polarization calculated for our monolayer model with $M=2(7)/3.6$, $s=-1$, and $V_{\text{S}}=-0.5\;\text{V}$. The inset shows the result after applying a low-pass filter. (f) Peak magnetic field from the spin polarization calculated for our monolayer model at various $M$, $s$, and $V_{\text{S}}$. Here, $M=2n/3.6$ accounts for $2n$ residues. Additional parameters are given in Sec. \ref{['Sec::Parameters']}.
• Figure 4: (a) Diagram (not to scale) showing treatment of each chiral molecule in our monolayer model as an $M$-turn solenoid with a current $I_{\text{peak}}$. Each solenoid is subsequently approximated as a point dipole with magnetic moment $\mu^z_{I} = s M\pi r^2 I_{\text{peak}}$. (b) Peak magnetic field from the peak current in our monolayer model, which was calculated by treating each chiral molecule as a point dipole according to panel (a), for various $M$, $s$, and $V_{\text{S}}$. Additional parameters are given in Sec. \ref{['Sec::Parameters']}.
• Figure 5: (a) $\lambda_0/t_0$ dependence of the maximum spin polarization at any site within a one-lead chiral molecule. (b) $\lambda_0/t_0$ dependence of the magnetic field from the spin polarization calculated for our monolayer model, depicted in Fig. \ref{['Fig::Experiment']}(d), with the peak magnetic field indicated. (c) $\lambda_0/t_0$ dependence of the peak magnetic field calculated for our monolayer model from the spin polarization (yellow), from the peak current (red), and from a uniform spin polarization $p_m(t) = \eta p_{\text{max}}(t)$, with $0.1\leq\eta\leq1.0$ (blue). The transient calculations used for panels (a), (b), and (c) apply $V_{\text{S}}$ at $t=0$ and use a fixed $t_0=0.2\;\text{eV}$ and $\Gamma_0=0.05\;\text{eV}$. Additional parameters are given by Sec. \ref{['Sec::Parameters']}. Adjusted results for the $\lambda_0/t_0$ dependence of the (d) maximum spin polarization, (e) magnetic field, and (f) peak magnetic field, now with $t_0=0.2\;\text{meV}$ and $\Gamma_0=0.05\;\text{meV}$ such that the transport timescale is slowed by a factor of 1000.