Luttinger-Kohn理论的多带哈密顿量和椭圆性要求
Multiband Hamiltonians of the Luttinger-Kohn Theory and Ellipticity Requirements
摘要：
现代应用需要一个强大的和理论上强大的工具，在低维纳米结构的电子态的逼真建模。$k \cdot p$理论自创立以来，在很长一段时间内都卓有成效地发挥了这一作用。在过去的二十年中，已经发现了与将$k \cdot p$方法应用于这种纳米结构有关的几个问题。这些问题与基础系统的椭圆率条件的违反密切相关，直到最近，这一事实在很大程度上被忽视了。我们表明，在许多情况下，由正式应用的Luttinger-Kohn理论推导出的模型不能满足椭圆度的要求。详细的分析，这里提出的一个例子的$6 \times 6$哈密顿，表明这种失败有很大的影响，对物理上的重要属性，传统上研究这些模型。
英文摘要：
Modern applications require a robust and theoretically strong tool for the realistic modeling of electronic states in low dimensional nanostructures. The $k \cdot p$ theory has fruitfully served this role for the long time since its creation. During last two decades several problems have been detected in connection with the application of the $k \cdot p$ approach to such nanostructures. These problems are closely related to the violation of the ellipticity conditions for the underlying system, the fact that until recently has been largely overlooked. We demonstrate that in many cases the models derived by a formal application of the Luttinger-Kohn theory fail to satisfy the ellipticity requirements. The detailed analysis, presented here on an example of the $6 \times 6$ Hamiltonians, shows that this failure has a strong impact on the physically important properties conventionally studied with these models.
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