Charge Redistribution and Spin Polarization Driven by Correlation Induced Electron Exchange in Chiral Molecules

Abstract

Chiral induced spin selectivity is a phenomenon that has been attributed to chirality, spin-orbit interactions, and nonequilibrium conditions, while the role of electron exchange and correlations have been investigated only marginally until very recently. However, as recent experiments show that chiral molecules acquire a finite spin-polarization merely by being in contact with a metallic surface, these results suggest that electron correlations play a more crucial role for the emergence of the phenomenon than previously thought. Here, it is demonstrated that molecular vibrations give rise to molecular charge redistribution and accompany spin-polarization when coupling a chiral molecule to a nonmagnetic metal. The presented theory opens up new routes to construct a comprehensive picture of enantiomer separation.

Keywords: chiral induced spin selectivity; electron−vibron coupling; exchange; spin-polarization.

Figure 1

Chiral molecule in (a) vacuum, (b) in contact with nonmagnetic metal, (c, d) in contact with ferromagnetic metals with opposite magnetizations. The diagrams illustrate the spin resolved molecular charge distributions, n_↑ (blue) and n_↓ (red). The black lines indicate the charge distribution in a vacuum.

Figure 2

Chiral molecule (8 × 6) in contact with a metallic surface. (a, b) Spin-resolved charge distribution and corresponding spin-polarization (⟨m_z⟩ = (n_↑– n_↓)/2) per site in the chiral molecule at the temperatures T = 20 mK and 300 K. In part a, the blue (cyan) and red (magenta) lines correspond to n_↑ and n_↓, respectively, at 300 K (20 mK). In part b, the blue (cyan) and red (magenta) lines represent positive (+) and negative (−) helicity, respectively, at 300 K (20 mK). (c) Spin-resolved charge distribution per site in the static chiral molecule at 20 mK (cyan, magenta) and 300 K (blue, red). (d) Spin-resolved charge distribution per site in the isolated vibrating chiral molecule at 20 mK (cyan, magenta) and 300 K (blue, red). (e, f) Charge and spin polarizations P_z and M_z, respectively, as a function of the number of sites, at 300 K. (f) Positive (negative) helicity is denoted by open (filled) hexagrams. Here, parameters used in the simulations are, in units of t₀ = 40 meV: ε₀ – E_F = −2, Γ₀ = 1/10, ω₀ = 1/100, λ₀ = 1/40, t₁ = 1/10, and λ₁ = 1/400, where E_F is the Fermi energy of the metal. An intrinsic broadening 1/τ_ph = t/4 was used in the vibration self-energy in order to smooth the electronic densities. In panel d, the long wavelength substructure is attributed to the numerical sensitivity to the integration mesh at low temperature.

Figure 3

Chiral molecule (8 × 6) in contact with a ferromagnetic surface. (a, b) Spin-resolved charge distribution for a molecule with (a) positive and (b) negative helicity. (c) Corresponding spin-polarization per site in the chiral molecule, for (blue) positive (+) and (red) negative (−) helicity. (d) Difference ⟨m_z⟩₊ – ⟨m_z⟩_– between the spin-polarizations for positive and negative helicity. (e, f) Charge and spin polarizations P_z and M_z, respectively, as a function of the number of sites, for positive (open symbols) and negative (filled symbols) helicity. Here, p = 0.1 and T = 300 K, while other parameters are as shown in Figure 2.

Figure 4

(a, b) Evolution of ⟨S_z⟩ of the local spin moment S under the self-consistent simulations for (a) 3 × 4 and 6 × 4 molecules and (b) 20 × 4 molecule. (c, d) Spin-resolved molecular charge distributions in the self-consistent limit for (c) positive (+) and (d) negative (−) helicity. (e) Spin-polarizations ⟨m_z⟩_± corresponding to the charge distributions in panels c and d. Maximum value of δ = ⟨S_z⟩₀ in the initial spin that can be switched for different molecules characterized by M × N. Here, ε₀ – E_F = −1/2, in panels c–f t₁ = 1/20, λ₀ = 1/10, λ₁ = 1/20, v = 1 in units of t₀, while other parameters and parameters in panel a are as shown in Figure 2.