一维狄拉克梳模型能带形成的数值和解析方法对比分析
COMPARISON OF NUMERICAL AND ANALYTICAL METHODS FOR ENERGY BAND OF THE ONE-DIMENSIONAL DIRAC COMB MODEL
邵怀华 1李晓波2
作者信息
- 1. 六盘水师范学院物理与电气工程学院,贵州 六盘水 553000
- 2. 海南大学物理与光电工程学院,海南 海口 570228
- 折叠
摘要
本文首先用空晶格模型讨论了周期性能带的形成;然后,在实空间推导了一维狄拉克梳模型的能量色散关系,结合数值模拟结果和近似方法公式系统地对比分析了能带的主要概念特征,图像直观地呈现了近自由电子近似下的能隙产生及其适用条件、紧束缚近似下的能带展宽等重要问题.用最简单的模型清楚地解析了两种近似下的能带形成图像.最后,给出了用平面波法对一维狄拉克梳模型特征能谱的收敛性分析,进一步验证了上述讨论.
Abstract
In this paper,we discuss the formation mechanism of energy band using the empty lattice model first.Then,we derive the energy dispersion of one-dimensional Dirac comb model in real space,and systematically compare and analyze the main conceptual characteris-tics of the energy bands by combining numerical simulation results and approximate method formulas.We clarify in more details about the physical significance of the nearly-free electron approximation and tight-binding approximation for band gap and bandwidth.Using the simp-lest models,we systematically give a visual image of energy band.Finally,a convergence a-nalysis of the plane-wave method is given for further explanation.
关键词
空晶格模型/狄拉克梳模型/能带/近自由电子近似/紧束缚近似Key words
empty lattice/Dirac comb/band structure/nearly-free electron approximation/tight-binding approximation引用本文复制引用
出版年
2024
国家科技期刊平台
NSTL
万方数据