Efficient electronic structure calculations for extended systems of coupled quantum dots using a linear combination of quantum dot orbitals method

We present a novel "linear combination of atomic orbitals"-type approximation, enabling accurate electronic structure calculations for systems up to 20 or more electronically coupled quantum dots. Using realistic single dot wavefunctions as basis expand the eigenstates heterostructure, our method shows excellent agreement with full 8-band $\boldsymbol{k}\cdot\boldsymbol{p}$ calculations, exemplarily chosen benchmarking comparison, an orders magnitude reduction in computational time. show that, order correctly predict properties such stacks dots, it is necessary consider strain distribution whole heterostructure. Edge effects determine $\lesssim$ 10 QDs, after which homogeneous confinement region develops center. The overarching goal investigations design stack vertically dots intra-band staircase potential suitable active material quantum-dot-based cascade laser. Following parameter study In$_{x}$Ga$_{1-x}$As/GaAs system, varying size, composition and inter-dot coupling strength, we that identical transitions can principle be realized. A species library generated over 800 unique provides easy access functions required different realizations heterostructures. In associated manuscript entitled "Room Temperature Lasing Terahertz Quantum Cascade Lasers Based on Dot Superlattice", investigate room temperature lasing terahertz laser based two-quantum-dot unit cell superlattice.