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

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.

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.

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.

These developments provide a robust foundation for scalable, physics-informed simulations of complex 2D systems and next-generation nanoelectronic devices.