  In this work, we theoretically investigate the light-induced topological
phases and finite-size crossovers in a paradigmatic quantum spin Hall (QSH)
system with high-frequency pumping optics. Taking the HgTe quantum well for an
example, our numerical results show that circularly polarized light can break
time-reversal symmetry and induce the quantum anomalous Hall (QAH) phase. In
particular, the coupling between the edge states is spin dependent and is
related not only to the size of the system, but also to the strength of the
polarized pumping optics. By tuning the two parameters (system width and
optical pumping strength), we obtain four transport regimes, namely, QSH, QAH,
edge conducting, and normal insulator. These four different transport regimes
have contrasting edge conducting properties, which will feature prominently in
transport experiments on various topological materials.
