Chirality-dependent second-order spin current in systems with time-reversal symmetry

The spin polarization phenomenon called chirality-induced spin selectivity (CISS) has recently attracted much attention. CISS was first discovered in DNA in 2011 and has been intensively studied in organic molecules. CISS in DNA has been reported to produce spin polarization rates of up to 60% and is expected to be applied to efficient spin current generation technology in the future. In 2020, it was shown that CrNb3S6, an inorganic crystal, also shows CISS.

Although the theory of CISS in organic materials has been intensively studied, it in inorganic materials remains to be explored. Since CISS is observed in the paramagnetic phase of CrNb3S6, spin polarization occurs in systems with time-reversal symmetry. However, it is known that a single-channel system with time-reversal symmetry does not produce a spin current linear in the electric field. This theorem makes the construction of the CISS theory difficult.

In this study, we constructed a chiral tight-binding model with time-reversal symmetry and evaluate its spin current. Specifically, we constructed a tight-binding model with chiral hopping and spin-orbit coupling and numerically calculated the spin currents proportional to the first and second orders of the electric field. As a result, it was found that the first-order spin current vanishes, while the second-order spin current can be finite. Furthermore, the sign of the second-order spin current can be reversed by switching the chirality of the model.