We present a novel “linear combination of atomic orbitals”-type of approximation, enabling accurate electronic structure calculations for systems of up to 20 or more electronically coupled quantum dots. Using realistic single quantum dot wave functions as a basis to expand the eigenstates of the heterostructure, our method shows excellent agreement with full 8-band $\mathit{k}·\mathit{p}$ calculations, exemplarily chosen for our benchmarking comparison, with orders of magnitude reduction in computational time. We show that, to correctly predict the electronic properties of such stacks of coupled quantum dots, it is necessary to consider the strain distribution in the whole heterostructure. Edge effects determine the electronic structure for stacks of $\lesssim 10$ quantum dots, after which a homogeneous confinement region develops in the center. The overarching goal of our investigations is to design a stack of vertically coupled quantum dots with an intraband staircase potential suitable as an active material for a quantum-dot-based quantum cascade laser. Following a parameter study in the ${\mathrm{In}}_x{\mathrm{Ga}}_{1-x}\mathrm{As}\text{/}\mathrm{GaAs}$ material system, varying quantum dot size, material composition, and interdot coupling strength, we show that an intraband staircase potential of identical transitions can, in principle, be realized. A species library we generated for over 800 unique quantum dots provides easy access to the basis functions required for different realizations of heterostructures. In the associated paper [Mittelstädt et al., Phys. Rev. B 103, 115301 (2021)], we investigate room temperature lasing of a terahertz quantum cascade laser based on a two-quantum-dot unit cell superlattice.

中文翻译：

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量子点轨道方法的线性组合用于耦合量子点扩展系统的有效电子结构计算

我们提出了一种新颖的“原子轨道的线性组合”类型的逼近，可为多达20个或更多个电子耦合量子点的系统进行精确的电子结构计算。以逼真的单量子点波函数为基础扩展异质结构的本征态，我们的方法显示出与全8波段的出色一致性$\mathit{ķ}·\mathit{p}$示例性选择用于我们的基准比较的计算，其计算时间减少了几个数量级。我们表明，要正确地预测耦合量子点的这种堆叠的电子性能，有必要考虑整个异质结构中的应变分布。边缘效应决定了电池堆的电子结构$\lesssim 10$量子点，然后在中心形成一个均匀的限制区域。我们研究的总体目标是设计一个带内阶梯电势的垂直耦合量子点堆栈，该量子点适合作为基于量子点的量子级联激光器的活性材料。在进行参数研究之后${在}_X{嘎}_{\mathrm{1个}-X}\mathrm{作为}\text{/}\mathrm{砷化镓}$在材料体系，变化的量子点尺寸，材料组成和点间耦合强度方面，我们证明，原则上可以实现相同跃迁的带内阶梯势。我们为800多个独特的量子点生成的物种库可轻松访问异质结构的不同实现所需的基本功能。在相关论文中[Mittelstädt等。，物理 版本B 103，115301（2021）]，我们研究室温基于双量子点晶胞超晶格的太赫兹量子级联激光器的激射。