Continuum model for chiral induced spin selectivity in helical molecules

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 spin-orbit coupling (SOC) opens up an effective π_z - π_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 (i) which spin orientation is selected depending on chirality and bias, (ii) changes in spin preference as a function of input Fermi level and (iii) back-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.