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Register a new userEffective Hamiltonian model for helically constrained quantum systems within adiabatic perturbation theory: application to the Chirality-Induced Spin Selectivity (CISS) Effect
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The chirality-induced spin selectivity (CISS) effect has been confirmed experimentally for a large class of organic molecules. Adequately modeling the effect remains a challenging task, with both phenomenological models and first-principle simulations yielding inconclusive results. Building upon a previously presented model by K. Michaeli and R. Naaman (J. Phys. Chem C 123, 17043 (2019)) we systematically investigate an effective 1-dimensional model derived as the limit of a 3-dimensional quantum system with strong confinement and including spin-orbit coupling. Having a simple analytic structure, such models can be considered a minimal setup for the description of spin-dependent effects. We use adiabatic perturbation theory to provide a mathematically sound approximation procedure applicable to a large class of spin-dependent continuum models. We take advantage of the models simplicity by analyzing its structure to gain a better understanding how the occurrence and magnitude of spin polarization effects relate to the models parameters and geometry.
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Dispersion interactions are one of the components of van der Waals forces, which play a key role in the understanding of intermolecular interactions in many physical, chemical and biological processes. The theory of dispersion forces was developed by London in the early years of quantum mechanics. However, it was only in the 1960s that it was recognized that for molecules lacking an inversion center such as chiral and helical molecules, there are chirality-sensitive corrections to the dispersion forces proportional to the rotatory power known from the theory of circular dichroism and with the same distance scaling law R-6 as the London energy. The discovery of the Chirality-Induced Spin Selectivity (CISS) effect in recent years has led to an additional twist in the study of chiral molecular systems, showing a close relation between spin and molecular geometry. Motivated by it, we propose in this investigation that there may exist additional contributions to the dispersion energy related to intermolecular, induced spin-orbit (ISOC) interactions. Within a second-order perturbative approach, these forces manifest as an effective intermolecular spin-spin exchange interaction. Although they are weaker than the standard London forces, the ISOC interactions turn out to be nevertheless not negligible and display the same R$^{-6}$ distance scaling. Our results suggest that classical force field descriptions of van-der Waals interactions may require additional modifications to include the effects discussed here.
We report a new type of spin-orbit coupling (SOC) called geometric SOC. Starting from the relativistic theory in curved space, we derive an effective nonrelativistic Hamiltonian in a generic curve embedded into flat three dimensions. The geometric SOC is $O(m^{-1})$, in which $m$ is the electron mass, and hence much larger than the conventional SOC of $O(m^{-2})$. The energy scale is estimated to be a hundred meV for a nanoscale helix. We calculate the current-induced spin polarization in a coupled-helix model as a representative of the chirality-induced spin selectivity. We find that it depends on the chirality of the helix and is of the order of $0.01 hbar$ per ${rm nm}$ when a charge current of $1~{rm mu A}$ is applied.
Chirality induced spin selectivity, discovered about two decades ago in helical molecules, is a non-equilibrium effect that emerges from the interplay between geometrical helicity and spin-orbit interactions. Several model Hamiltonians building on this interplay have been proposed and while these can yield spin-polarized transport properties that agrees with experimental observations, they simultaneously depend on unrealistic values of the spin-orbit interaction parameters. It is likely, however, that a common deficit originates from the fact that all these models are uncorrelated, or, single-electron theories. Therefore, chirality induced spin selectivity is, here, addressed using a many-body approach, which allows for non-equilibrium conditions and a systematic treatment of the correlated state. The intrinsic molecular spin-polarization increases by two orders of magnitudes, or more, compared to the corresponding result in the uncorrelated model. In addition, the electronic structure responds to varying external magnetic conditions which, therefore, enables comparisons of the currents provided for different spin-polarizations in one of the (or both) leads between which the molecule is mounted. Using experimentally feasible parameters and room temperature, the obtained normalized difference between such currents may be as large as 5 - 10 % for short molecular chains, clearly suggesting the vital importance of including electron correlations when searching for explanations of the phenomenon.
Here we propose a mechanism by which spin polarization can be generated dynamically in chiral molecular systems undergoing photo-induced electron transfer. The proposed mechanism explains how spin polarization emerges in systems where charge transport is dominated by incoherent hopping, mediated by spin orbit and electronic exchange couplings through an intermediate charge transfer state. We derive a simple expression for the spin polarization that predicts a non-monotonic temperature dependence consistent with recent experiments. We validate this theory using approximate quantum master equations and the numerically exact hierarchical equations of motion. The proposed mechanism of chirality induced spin selectivity should apply to many chiral systems, and the ideas presented here have implications for the study of spin transport at temperatures relevant to biology, and provide simple principles for the molecular control of spins in fluctuating environments.
The theoretical explanation for the chiral-induced spin selectivity effect, in which electrons passage through a chiral system depends on their spin and the handedness of the system, remains vague. Although most experimental work was performed at room temperature, most of the proposed theories did not include vibrations. Here, we present temperature-dependent experiments and a theoretical model that captures all observations and provides spin polarization values that are consistent with the experimental results. The model includes vibrational contribution to the spin orbit coupling. It shows the importance of dissipation and the relation between the effect and the optical activity.
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