  Transport phenomena of microswimmers in fluid flows play a crucial role in
various biological processes, including bioconvection and cell sorting. In this
paper, we investigate the dispersion behavior of chiral microswimmers in a
simple shear flow utilizing the generalized Taylor dispersion (GTD) theory,
motivated by biased locomotion of bacterial swimmers known as bacterial
rheotaxis. We thus focus on the influence of shear-induced torque effects due
to particle chirality, employing an extended Jeffery equation for individual
deterministic dynamics. We then numerically calculate macroscopic parameters
including averaged swimming velocity and effective diffusion tensor using
spherical harmonic expansion, and argue the obtained results based on the fixed
points and their stability of the orientational dynamical systems. Our results
reveal that chiral effects induce biased locomotion and we observe qualitative
transitions in the orientational distribution with increasing Pecl\'et number,
aligning with previous experimental findings. The diffusion tensor analysis
highlights significant reduction in the diffusion coefficient perpendicular to
the flow plane due to chirality. This suggests potential applications in
flow-mediated cell separation and we numerically demonstrate such
chirality-induced fluid transportation. The presented methods will be useful in
predicting and controlling dispersion behaviors of such chiral microswimmers.
