Topological Charge-2ne Superconductivity and Clustering Hierarchy

Charge- 2ne superconductors condense clusters of more than two electrons, extending superconductivity beyond Cooper pairing. They exhibit distinctive signatures including fractional flux quantization h/(2ne) and are actively being explored in strongly correlated systems. We develop a general framework for constructing and characterizing topological charge- 2ne superconductors by combining wavefunction and field theory approaches. Generalizing the Read-Green wavefunction and Higgsing Read-Rezayi-type states yield two families that can support deconfined non-Abelian anyons and non-Abelian superconducting vortices. The first family also admits a construction from doping Jain states. Through Higgs theories, we find that the first and second families realize weak and intermediate clustering regimes, respectively, distinguished by the topology of vortices carrying flux greater than h/(2ne), while strong clustering yields a charge- 2ne superconductor without intrinsic topological order. These reveal that higher-charge superconductivity supports a richer hierarchy of topological phases beyond the Read-Green weak-strong pairing dichotomy, with distinct internal clustering structures giving rise to different topological structures at fixed condensate charge.