Single-valley engineering in graphene superlattices

The two inequivalent valleys in graphene are protected against long-range scattering potentials due to their large separation in momentum space. In tailored √3N×√3N or 3N×3N graphene superlattices, these two valleys are folded into Γ and coupled by Bragg scattering from periodic adsorption. We find that, for top-site adsorption, strong intervalley coupling closes the bulk gap from inversion symmetry breaking and leads to a single-valley metallic phase with quadratic band crossover. The degeneracy at the crossing point is protected by C₃ᵥ symmetry. In addition, the emergence of pseudo-Zeeman field and valley-orbit coupling are also proposed, which provide the possibility of tuning valley polarization coherently in analogy to real spin for spintronics. Such valley manipulation mechanisms can also find applications in honeycomb photonic crystals. We also study the strong geometry-dependent influence of hollow- and bridge-site adatoms in the intervalley coupling.