Analytic Model of Chiral-Induced Spin Selectivity

Abstract

Organic materials are known to feature long spin-diffusion times, originating in a generally small spin-orbit coupling observed in these systems. From that perspective, chiral molecules acting as efficient spin selectors pose a puzzle that attracted a lot of attention in recent years. Here, we revisit the physical origins of chiral-induced spin selectivity (CISS) and propose a simple analytic minimal model to describe it. The model treats a chiral molecule as an anisotropic wire with molecular dipole moments aligned arbitrarily with respect to the wire's axes and is therefore quite general. Importantly, it shows that the helical structure of the molecule is not necessary to observe CISS and other chiral nonhelical molecules can also be considered as potential candidates for the CISS effect. We also show that the suggested simple model captures the main characteristics of CISS observed in the experiment, without the need for additional constraints employed in the previous studies. The results pave the way for understanding other related physical phenomena where the CISS effect plays an essential role.

Figure 1

Pictorial representation of the molecule: (a) As a helix used in the previous studies and (b) As a finite quantum wire employed in this study. Implementation of two enantiomers with finite quantum wire potential is also shown. Electrons are depicted as red and yellow spheres, where color and arrows are related to the spin of the particles. μ_x, μ_y, and μ_z are different components of the dipole field of the molecule. (c) Graphical representation of the scattering events considered in eq 4.

Figure 2

Dependence of the outgoing beam spin polarization in the z direction (a) on the polar angle θ and (b) on the incoming electron energy when integrated over θ in the range [0−π/2], for different angles of incoming polar angle α. The incoming electron energy is 1000 meV in (a); the results are integrated over both incoming and outgoing azimuthal angles β and τ.

Figure 3

(a) Dependence of the outgoing beam spin polarization in the z direction on the length of the molecule l_z, for different angles of incoming polar angle, α. The results are integrated over outgoing polar angle θ and in the incoming and outgoing azimuthal angles β and τ. (b) Dependence of the fully integrated outgoing beam spin polarization in the z direction on the length of the molecule l_z and energy of incoming electrons. The integration range for polar angles is again [0, π/2] and for azimuthal angles [0, 2π]. The electron energy is 1000 meV for the length dependence curves.