(a) Contour of Berry curvature distribution in (k_x, k_y) plane for the valley-polarized QAH effect. (b) Berry curvature distribution as a function of k_x at fixed k_y = 2π/√3. (c) The band structure of zigzag-terminated silicene exhibiting the valley-polarized QAH effect, where colors are used to label the edge modes localized at the opposite boundaries. (d) Valley-associated edge modes for the valley-polarized QAH effect. Reprinted with permission from Ref. [61]. Copyright 2014 by the American Physical Society.