The affection on the nature of percolation by concentration of pentagon-heptagon defects in graphene lattice

In this paper the percolation behavior with a specific concentration of the defects was discussed on the two-dimensional graphene lattice. The percolation threshold is determined by a numerical method with a high degree of accuracy. This method is also suitable for locating the percolation critical point on other crystalline structures. Through investigating the evolution of the largest cluster size and the cluster sizes distribution, we find that under various lattice sizes and concentrations of pentagon-heptagon defects there is no apparent change for the percolation properties in graphene lattice.