▎ 摘　　要

The graphene nanoscrolls (GNS) are an open edge rolled up of a graphene sheet which shows unique electrical properties. The electronic structure of the GNS with respect to the automatic formation of GNS due to the Van der Waals interaction has been studied and the bending energy of the graphene sheet has been discussed. The objective of this paper is to find out the geometry effect on band structure of a one dimensional GNS and its periodic boundary condition 2 pi nu - theta effect in band energy is considered. The density of states (DOS) in proposed boundary condition for one dimensional GNS is established and numerically simulated by MATLAB. Moreover the DOS gradient by variation of theta is reported and the energy band model near the Fermi level is computed. The method to engineer the GNS band gap for future nanoelectronic fabrication is discussed.