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

TL;DR

This paper demonstrates that in systems with time-reversal symmetry, second-order spin currents depend on chirality and can be finite, while first-order spin currents vanish, revealing chirality-dependent spin polarization phenomena.

Contribution

It introduces a tight-binding model with chiral hopping and spin-orbit coupling showing chirality-dependent second-order spin currents in time-reversal symmetric systems.

Findings

First-order spin current vanishes.

Second-order spin current is finite and chirality-dependent.

Reversing chirality changes the sign of the spin current.

Abstract

Spin currents proportional to the first- and second-order of the electric field are calculated in a specific tight-binding model with time-reversal symmetry. Specifically, a tight-binding model with time-reversal symmetry is constructed with chiral hopping and spin-orbit coupling. The spin conductivity of the model is calculated using the Boltzmann equation. As a result, it is clarified that the first-order spin current of the electric field vanishes, while the second-order spin current can be finite. Furthermore, the spin current changes its sign by reversing the chirality of the model. The present results reveal the existence of spin currents in systems with time-reversal symmetry depending on the chirality of the system. They may provide useful information for understanding the chirality-dependent spin polarization phenomena in systems with time-reversal symmetry.