Integer quantum Hall effect in Kekule-patterned graphene

Y-shaped Kekule 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 Kekule-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 Kekule 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 +/- ne (2)/h for n = 2, 4, 6, 8, 10, horizontal ellipsis , 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 Kekule bond texture amplitude.

Automated summary

This paper investigates the effects of Y-shaped Kekule bond texture on the transport coefficients of Kekule-patterned graphene. It is found that this texture lifts the valley degeneracy of all levels except the zero mode, resulting in additional plateaus in the Hall conductivity and a split of the peaks in the longitudinal conductivity. The results also indicate that DC Hall conductivity measurements can determine the amplitude of the Kekule bond texture.