Advanced Quantum Models for Corrugation and Defects in Two-Dimensional Materials

<p dir="ltr">Modeling complex two-dimensional (2D) systems requires strategies that move beyond conventional assumptions of periodicity and scalability in atomistic simulations. As system sizes grow or structural inhomogeneities such as corrugation and atomic-scale defects arise, standard first-principles methods often become computationally prohibitive. To address these challenges, this work develops two advanced quantum modeling approaches.</p><p dir="ltr">The first introduces a self-adaptive parameter optimization scheme for the Density Functional Tight Binding (DFTB) method, utilizing hybrid-functional Density Functional Theory (DFT) as a reference. This genetic algorithm-based workflow enables the accurate simulation of large periodic systems, as demonstrated through the piezoelectric response of twisted van der Waals (vdW) heterobilayers.</p><p dir="ltr">The second extends the capabilities of quantum transport simulations via the Recursive Open Boundary and Interface (ROBIN) method, allowing for the analysis of spatially disordered, non-periodic systems, such as defective monolayers. Simulations reveal that periodic defect arrangements give rise to artificial mid-gap states due to coherent coupling. In contrast, randomized defect configurations produce broadened, non-resonant spectral features that more closely represent realistic disorder.</p><p dir="ltr">These developments provide a robust foundation for scalable, physics-informed simulations of complex 2D systems and next-generation nanoelectronic devices.</p>