Designing artificial moiré van der Waals topological superconductivity

The study of topological superconductivity is a promising field in condensed matter physics that has exciting possibilities for the emergence of exotic quantum phenomena and topological quantum computing. In this thesis, we investigate various platforms for engineering topological superconductivity, focusing on the role of quasiperiodicity and van der Waals materials featuring moiré patterns. The first scheme concentrates on quasiperiodic systems and their capability to generate robust spin-triplet superconducting pairings through coexisting orders, establishing a new strategy for engineering unconventional superconductivity. In the second scheme, we focus on specific van der Waals heterostructures showing moiré patterns. We examine the role of impurities in designer topological moiré superconductors that combine van der Waals magnetic and superconducting materials, focusing on the interplay between atomic and moiré length scales within these artificial moiré systems explored with conventional tools and machine learning. In the third scheme, we focus on hybrid van der Waals heterostructures based on twisted graphene bilayers, magnets, and superconductors, establishing their potential as a versatile platform for engineering artificial topological  superconductivity.Our results showcase the potential of designer platforms, such as quasiperiodicity and moiré-patterned van der Waals materials, to harness and manipulate these intriguing quantum states. Our findings establish new strategies for developing quantum technologies based on topological superconducting quantum materials and further enrich our understanding of exotic quantum matter.