Evolution of band structures of bulk graphene along the profile of k_y = 0. The arrows represent the spin directions. (a) Pristine graphene: spin-up and spin-down states are degenerate; (b) when only exchange field λ = 0.4 is applied, the spin-up/spin-down bands are upward/downward lifted with the four bands crossing near K and K′ points; (c) when only Rashba SOC t_SO = 0.1 is present, the spin-up and spin-down states are mixed around the band crossing points; (d) when both exchange field λ = 0.4 and Rashba SOC t_SO = 0.1 are present, a bulk gap is opened and all four bands become nondegenerate. Reprinted with permission from Ref. [12]. Copyright 2010 by the American Physical Society.