固体物理教学的若干思考Ⅰ:多轨道紧束缚近似  

Some thoughts on teaching solid state physics Ⅰ:the tight-binding approximation with multiple orbitals

作　　者：袁喆 YUAN Zhe(Department of Physics,Beijing Normal University,Beijing 100875,China)

机构地区：[1]北京师范大学物理学系,北京100875

出　　处：《大学物理》2020年第12期1-4,27,共5页College Physics

基　　金：中央高校基本科研业务费专项资金(2018EYT03)资助。

摘　　要：紧束缚近似是固体能带理论教学中的重要内容,其中包含很多重要的概念和物理图像.目前教材中的紧束缚近似多采用单轨道例子,导致教学中对哈密顿量、能带、布洛赫波函数等概念缺乏深刻理解.本文采用了一维双原子链模型,详细阐述了如何求解多轨道紧束缚近似下晶体的能带,并借助构建哈密顿量的数学过程,展示了紧束缚近似下原子能级微扰、近邻原子轨道交叠积分等物理图像,讨论了能带走势与布洛赫波函数的关系,以及影响能带个数与能带宽度的因素.The tight binding approximation is one of the most important parts in the teaching of energy band theory,which contains many key concepts of solid state physics and intuitive pictures.Most of the popular textbooks only illustrate the tight-binding approach by using single-band examples.Then it becomes difficult for students to comprehend the Hamiltonian,energy bands,Bloch wave functions and the related concepts.Here a one-dimensional diatomic linear chain is solved with a detailed elucidation for how to obtain the energy bands with multiple orbitals using the tight-binding approximation.The perturbation of atomic energy level and overlap integral of neighboring atomic orbitals are illustrated in the mathematical derivation of the tight-binding Hamiltonian.The energy band dispersion with the relationship to the Bloch wave functions is discussed as well as the factors that determine the number of bands and band widths.

关 键 词：固体物理 紧束缚近似 能带理论 

分 类 号：O481[理学—固体物理]