Integer quantum Hall effect in Kekulé-patterned graphene

Y-shaped Kekulé bond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed. In this paper, the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field. Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula. It is found that the Y-shaped Kekulé bond texture lifts the valley degeneracy of all Landau levels except that of the zero mode, leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity. Consequently, the Hall conductivity is quantized as ±ne²/h for n=2, 4, 6, 8, 10,..., excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones. These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulé bond texture amplitude.