  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.
