Collective resonances near zero energy induced by a point defect in bilayer graphene

Jhih-Shih You, Jian-Ming Tang, Wen-Min Huang

Published 2017-10-18Version 1

Intrinsic defects give rise to scattering processes governing the transport properties of mesoscopic systems. We investigate analytically and numerically the local density of states in Bernal stacking bilayer graphene with a point defect. From this theoretical study, a picture emerges in which the pronounced zero-energy peak in the local density of states does not attribute to zero-energy impurity states associated to two different types of defects, but to a collective phenomenon of the low-energy resonant states induced by the defect. To corroborate this description, we numerically show that at small system size $N$, the zero-energy peak near the defect scales as $1/\ln N$ for the quasi-localized zero-energy state and as $1/N$ for the delocalized state. As the system size approaches to the thermodynamic limit, the former zero-energy peak becomes a power-law singularity $1/|E|$ in low energies, while the latter is broadened into a Lorentzian shape. A striking point is that both types of zero-energy peaks decay as $1/r^2$ away from the defect, manifesting the quasi-localized character. Based on our results, we propose a general formula for the local density of states in low-energy and in real space. Our study sheds light on this fundamental problem of defects.