Poster Title: 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 Chern insulator Qi-Wu-Zhang (QWZ) model. Using computational methods, I plotted the band structure of these insulators by solving the Schrödinger's equation using the Hamiltonians of each model. By manipulating the initial conditions, I was able to demonstrate the properties of topological insulators. I also analyzed how these models behave after applying a dislocation. The results confirm the predicted edge state behavior of both the SSH as well as showing the unique properties of the QWZ model regarding dislocations which present an interesting candidate for qubits.