Atomic geometry and band structures of the graphene/Au/Ni (111) heterostructure. (a) Side and top views of the atomic structure of the graphene/Au/Ni (111) heterostructure. The gray, red, and blue balls respectively denote the C, Au, and Ni atoms. All of the Au atoms are on the top sites of a specific sub-lattice. Valley-resolved band structures of the graphene/Au/Ni heterostructure for M ∥ X (b) and M ∥ Z (c). The black, blue, and red dotted lines represent the orbital contributions of the p orbits of the C atoms, the 3d orbits of the Ni atoms, and 5d orbits of Au, respectively. The red rectangles in (b) and (c) are replotted in the right to show the valley splitting.