Bulk band structures of graphene on BiFeO₃. (a) Spin-resolved band structures. (b) Zoom in on the green box of panel (a). The blue (thin) and red (thick) lines in panels (a) and (b) represent the spin-up and spin-down bands, respectively. (c) Band structure when the spin–orbit coupling is included. A bulk gap δ of about 1.1 meV is centered on the avoided crossings near the K and K′ valleys. Note that the nontrivial band gap δ is inside the bulk gap Δ of BiFeO₃. (d) Zoom in on the green box of panel (c). Reprinted with permission from Ref. [16]. Copyright 2014 by the American Physical Society.