Superconductivity is a uniquely quantum mechanical phenomenon that despite decades of intense research is still very hard to control. It is heavily dependent on the density of states (DOS) around zero energy, but this DOS tunability has so far remained largely untapped. This project aims to theoretically create and enhance superconductivity by producing large DOS peaks at zero energy using nanoscale inhomogeneity, thereby creating an entirely new, spatial and figurative, landscape for superconductivity. A rare, not yet understood, example is twisted bilayer graphene, an all-carbon material not assumed to be superconducting. Here small twist angles produce an inhomogeneous moiré structure hosting large zero-energy DOS peaks that have recently been shown to create superconductivity. In this project we will understand, as well as enhance, superconductivity in moiré structures in both graphene and topological insulators. In this project we will also establish superconductivity driven entirely by other types of nanoscale inhomogeneity generating zero-energy DOS peaks. We will also use zero-energy DOS peaks to create a superconducting phase crystal in different superconductors, generalizing findings from high-temperature cuprate superconductor surfaces. Due to its nanoscale phase modulations and spontaneous supercurrents, the phase crystal dramatically enriches the superconducting properties. To succeed with this project, we will use and further develop our own state-of-the-art numerical tools to self-consistently study superconductivity at the atomistic level in very large inhomogeneous systems. Taken together, this project will create an entirely new, inhomogeneous, landscape for superconductivity.
