Symmetry-Based Model Hamiltonians for Topological Analysis of 2D Materials with Square Lattice

Classes of symmetry-based model Hamiltonians can be constructed with specific point group restrictions. These models combine the flexibility of tight-binding models with the analytical simplicity of the Su-Schrieffer-Heeger model and can be scaled in either direction. The applicability of models with two, three, and four bands to topological analysis is investigated and limitations to describing topological behaviour are assessed. The models are applied to fitting density functional theory (DFT) band structures for selected 2D materials with and without spin-orbit coupling. Suitable parameters for selected materials are obtained and used to describe the topological phase of the materials. Based on these results, a single two-, three-, and four-band model is found which describes the band structure and topological properties of all the selected 2D materials. Suitable simplifications to the models are outlined to further illustrate how the analyzability can be scaled with the accuracy of the model. While generally a higher degree of symmetry helps the formation of topological phases, extremely symmetric point groups like D 4h $D_{\text{4h}}$ restrict the allowed interactions to a degree that makes topological phases less easy to achieve.