Valley-momentum locking in a graphene superlattice with Y-shaped Kekulé bond texture

Recent experiments by Gutiérrez et al (2016 Nat. Phys. 12 950) on a graphene–copper superlattice have revealed an unusual Kekulé bond texture in the honeycomb lattice—a Y-shaped modulation of weak and strong bonds with a wave vector connecting two Dirac points. We show that this so-called 'Kek-Y' texture produces two species of massless Dirac fermions, with valley isospin locked parallel or antiparallel to the direction of motion. In a magnetic field B, the valley degeneracy of the B-dependent Landau levels is removed by the valley-momentum locking but a B-independent and valley-degenerate zero-mode remains.