SC: superconductivity intertwined with topological order
The work develops a classification framework for (2+1)D gapped superconductors by analyzing the topological properties of superconducting vortices. This leads to five classes: invertible SC, SC*, twisted SC*, SC#, and primitive SC#. The key finding is that the 'SC#' phase represents a fundamental intertwining where elementary vortices are intrinsically non-Abelian, leading to no-go results like quantum dimension constraints.