Superconductivity in Fractal Lattices

Quantum behavior in exotic geometries has become the subject of theoretical and experimental research due to progress in the field of synthetic quantum systems. In this project, we will theoretically consider fractal lattices, and ask how this geometry affects superconductivity, and in particular topological superconductivity. Through this project, the student will learn about these important condensed matter phenomena and how to describe them theoretically using mean-field theory. The student will also develop computer code to numerically study the mean-field equations, and obtain novel insight in the role of geometry by comparing the solutions in fractal and regular lattices.