Abstract

The electron spectrum in a uniform nanowire with a hexagonal cross-section is calculated by means of a numerical diagonalization of the effective-mass Hamiltonian. Two basis sets are utilized. The wave-functions of low-lying states are calculated and visualized. The approach has an advantage over mesh methods based on finite-differences (or finite-elements) schemes: non-physical solutions do not arise. Our scheme can be easily generalized to the case of multi-band (Luttinger or Kane) k ⋅ p Hamiltonians. The external fields (electrical, magnetic or strain) can be consistently introduced into the problem as well.

中文翻译：

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具有六角形截面的纳米线中的电子态

摘要

通过有效质量哈密顿量的对角线化计算出具有六边形横截面的均匀纳米线中的电子光谱。使用了两个基集。计算并可视化低洼状态的波函数。与基于有限差分（或有限元）方案的网格方法相比，该方法具有优势：不会出现非物理解。我们的方案可以容易地推广到多频带（Luttinger或凯恩）的情况下ķ ⋅ p汉密尔顿。外部磁场（电场，磁场或应变）也可以始终如一地引入到问题中。