Evolution of the sub-band structure upon increasing the exchange field. The solid lines denote the sub-bands that have even parity at Γ point, and the dashed lines denote the sub-bands with odd parity at Γ point. The blue (red) color denotes the spin-down (spin-up) electrons. (a) The initial sub-bands are not inverted. When the exchange field is strong enough, a pair of inverted sub-bands appear (red dashed line and blue solid line). (b) The initial sub-bands are already inverted. The exchange field releases the band inversion in one pair of sub-bands (red solid line and blue dashed line) and increases the band inversion in the other pair (red dashed line and blue solid line). Reprinted with permission from Ref. [11]. Copyright 2010 by the American Association for the Advancement Science.