ABSTRACT
We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort.
ABSTRACT
We have developed a highly efficient computation method based on density functional theory (DFT) within a set of fully symmetrized basis functions for the C60 buckyball, which possesses the icosahedral (Ih) point-group symmetry with 120 symmetry operations. We demonstrate that our approach is much more efficient than the conventional approach based on three-dimensional plane waves. When applied to the calculation of optical transitions, our method is more than one order of magnitude faster than the existing DFT package with a conventional plane-wave basis. This makes it very convenient for modeling optical and transport properties of quantum devices related to buckyball crystals. The method introduced here can be easily extended to other fullerene-like materials.
