Continuum model for chiral induced spin selectivity in helical molecules

TL;DR

This paper presents an exactly solvable continuum model for electron spin transport in chiral helical molecules, revealing how chirality, bias, and SOC influence spin selectivity and current, with implications for understanding CISS effects.

Contribution

It introduces a minimal, exactly solvable continuum model that captures spin transport and selectivity in chiral molecules, linking structure, bias, and SOC effects.

Findings

Transport channels are Kramers doublets with a SOC-induced gap.

Spin orientation depends on chirality and bias direction.

Spin current is proportional to the molecule's torsion and Aharonov-Anandan phase.

Abstract

A minimal model is exactly solved for electron spin transport on a helix. Electron transport is assumed to be supported by well oriented $p_z$ type orbitals on base molecules forming a staircase of definite chirality. In a tight binding interpretation, the SOC opens up an effective $\pi_z-\pi_z$ coupling via interbase $p_{x,y}-p_z$ hopping, introducing spin coupled transport. The resulting continuum model spectrum shows two Kramers doublet transport channels with a gap proportional to the SOC. Each doubly degenerate channel satisfies time reversal symmetry, nevertheless, a bias chooses a transport direction and thus selects for spin orientation. The model predicts which spin orientation is selected depending on chirality and bias, changes in spin preference as a function of input Fermi level and scattering suppression protected by the SO gap. We compute the spin current with a definite helicity and find it to be proportional to the torsion of the chiral structure and the non-adiabatic Aharonov- Anandan phase. To describe room temperature transport we assume that the total transmission is the result of a product of coherent steps limited by the coherence length.