Computationally Modeling Topological Insulators*

In recent years, topological insulators have garnered significant attention due to their promising applications in nanoelectronics and potential roles in quantum supercomputing. This study examines tight binding models of topological insulators; specifically focusing on the one dimensional Su-Schrieffer-Heeger (SSH) model and the two dimensional Qi-Wu-Zhang (QWZ) model. Using computational methods, I modeled the energy bands of these insulators by representing the real space Hamiltonians of each model and solving Schrödinger's equation. Through this approach, I was able to plot the energy spectra and analyze the wavefunctions, demonstrating that these materials conduct at their boundaries. I also analyzed these models after applying a dislocation to the lattice. Our results confirm the predicted edge state behavior of both the SSH and QWZ models as well as showing the unique properties of the QWZ model in regards to dislocations. These findings contribute to a deeper understanding of the properties of topological insulators, providing a crucial step towards their practical implementation in advanced technological applications. This research underscores the importance of computational models in the study of quantum materials, highlighting their potential in the development of future nanoelectronic and quantum computing devices.