Modeling high-order harmonic generation in quantum dots using a real-space tight-binding approach

Recently, the size-dependence of high-order harmonic generation (HHG) in quantum dots has been investigated experimentally. In particular, for longer driving wavelengths and QDs smaller than 3\,nm, HHG was strongly suppressed, however, there is no computational model capable of describing the strong-field response of such systems. In this work, we introduce a computationally efficient three-dimensional real-space tight-binding model specifically designed for the simulation of HHG in confined systems. The model parameters are meticulously derived from density functional theory (DFT) calculations for the semiconductor bulk, followed by a process of Wannierization. Our findings demonstrate that the proposed model accurately captures the observed dependency of the HHG yield on the quantum dot size. Additionally, we simulate the HHG yield for elliptically polarized pulses for different QD-sizes and driving wavelengths up to $5\,\mu{\mathrm{m}}$. The herein proposed model fills the theoretical void in simulating HHG within medium-sized nanostructures, which cannot be described by methods applied for periodic solids or small molecules or atoms.