Density Functional Theory and Tight-Binding Models

This lecture covers the motivation behind modeling and simulating multilayer 2D materials, including graphene and transition metal dichalcogenides. It explores the multiscale approach, from first-principle calculations to tight-binding models, to predict electronic and optical properties. The Quantum Drude model and Kubo formula are discussed for understanding electrical conductivity in materials. The lecture also delves into the construction of reduced tight-binding models for multilayer 2D materials, emphasizing the importance of symmetries in obtaining accurate results. Mathematical results regarding Wannier functions and Gaussian-type orbitals are presented, along with practical computations of conductivity. The conclusion highlights the transition from first-principle calculations to mesoscopic/macroscopic models for homogeneous and disordered materials.