Kernel polynomial method to Anderson transition in disordered $\beta$-graphyne.

By means of variable moment kernel polynomial method, we analyze the localization properties of $\beta$-graphyne sheet subjected to the Anderson disorder. To detect the localization transition we focus on the scaling behavior of the normalized typical density of states. We find that there takes place a metal-insulator transition and the critical disorder strength is of the order of the bandwidth, which is contrary to the one-parameter scaling theory stating that for infinite two dimensional systems, all the electronic states are localized for an arbitrary strength of the Anderson disorder. As its particular localization properties, it is reasonable to predict there will exist dc conductivity for $\beta$-graphyne at zero temperature.