Spin-Current and Spin-Splitting in Helicoidal Molecules Due to Spin-Orbit Coupling

Abstract

The use of organic materials in spintronic devices has been seriously considered after recent experimental works have shown unexpected spin-dependent electrical properties. The basis for the confection of any spintronic device is ability of selecting the appropriated spin polarization. In this direction, DNA has been pointed out as a potential candidate for spin selection due to the spin-orbit coupling originating from the electric field generated by accumulated electrical charges along the helix. Here, we demonstrate that spin-orbit coupling is the minimum ingredient necessary to promote a spatial spin separation and the generation of spin-current. We show that the up and down spin components have different velocities that give rise to a spin-current. By using a simple situation where spin-orbit coupling is present, we provide qualitative justifications to our results that clearly point to helicoidal molecules as serious candidates to integrate spintronic devices.

Figure 1. Illustration of a double-strand DNA molecule with radius R, helix angle θ and pitch h.

The nucleobases are represented by the circles. The arc length between two neighboring nucleobases is l_a, which satisfies the relation l_a cosθ = RΔφ and l_a sinθ = Δh, where Δφ is the twist angle and Δh is stacking distance between two nucleobases. In order to mimic the double-strand DNA molecule, we set Δh = 0.34 nm, Δφ = π/5, h = 3.4 nm, R = 0.7 nm, θ ≈ 0.66 rad and l_a ≈ 0.56 nm.

Figure 2. Time evolution of an initially gaussian wave packet, with l = 30, for different times: t₁ = 0.4 ps, t₂ = 0.65 ps and t₃ = 0.86 ps.

The wave packet evolves in a double strand molecule described by the parameters: , , , η = 0.3 eV, θ = 0.66 and and t_SO = 0.03 eV. The up and down spinor components are represented by red and blue, respectively.

Figure 3

Time evolution of the mean position, defined by: and , of an initially gaussian wave packet, in a double strand molecule, with width (a) l = 1 and (b) l = 30 for three spin-orbit coupling constant: t_so = 0.01, t_so = 0.02 and t_so = 0.03 eV. (c,d) are, respectively, the mean velocity of the wave packet components for the cases studied in (a,b).

Figure 4

(a,b) show the time evolution of the spin current for an initially unpolarized gaussian wave packet in a single strand helicoidal molecule, with l = 1 and l = 30, respectively, for spin-orbit coupling, t_so, equal to 0.01, 0.02 and 0.03 eV.

Figure 5

(a,b) show the time evolution of ζ function for an initially unpolarized gaussian wave packet in a single strand helicoidal molecule, with l = 1 and l = 30, respectively, for spin-orbit coupling, t_so, equal to 0.01, 0.02 and 0.03 eV. (c,d) show, respectively a snapshot of the absolute squared of the wave packet at t = 0.49 ns of the initial wave packet with l = 1 and l = 30 and t_so = 0.03 eV.