Modeling graphene layers and single-walled carbon nanotubes with regularized δ-function potentials

In this paper, a model is proposed to simulate the π electrons in a graphene layer and single-walled carbon nanotubes. We let the atomic potential of each carbon atom be replaced by a two-dimensional attractive regularized δ function and construct a honeycomb lattice of regularized δ functions to reproduce the band structure of a graphene layer and nanotubes. Our results are in good agreement with first principle calculations. We also use this model to calculate the electron wave functions of nanotubes with finite length. The results are also in agreement with first principle calculations. With the accuracy and simplicity provided by this model, it is a good candidate to study the interaction between the π electrons of nanotubes and electromagnetic fields in nonperturbative regime.