Paudel Raj Kumar, Ren Chung-Yuan, Chang Yia-Chung
Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan.
Molecular Science and Technology, Taiwan International Graduate Program, Academia Sinica, Taipei 11529, Taiwan.
Nanomaterials (Basel). 2023 Jul 13;13(14):2066. doi: 10.3390/nano13142066.
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.
我们实现了一种半经验赝势（SEP）方法来计算石墨烯和石墨烯纳米带的能带结构。所采用的基函数是二维平面波乘以沿垂直方向的几个B样条函数。SEP包括局部和非局部项，这些项通过参数化来拟合基于密度泛函理论（DFT）的第一性原理计算得到的相关量。仅用少量参数，我们就能以可忽略不计的差异重现DFT得到的石墨烯完整能带结构。我们的方法使用简单，且比DFT计算效率高得多。然后我们应用这种SEP方法来计算石墨烯纳米带的能带结构。通过在纳米带边缘的局部赝势上添加一个简单的校正项（模拟边缘产生的效应），我们再次得到了扶手椅型纳米带的能带结构，其与DFT得到的结果相当接近。我们的方法只需极少的计算量就能模拟由石墨烯纳米带制成的实际纳米器件的光学和输运性质。
