Topological Charge-4e Superconductor

Charge-4e superconductors exemplify a class of intrinsically correlated phase of matter, admitting no noninteracting description even at mean field level. They typically appear as vestiges of charge-2e states, most notably the pair density waves. In rare cases, they can arise as primary quartetting orders. We term the former as reducible charge-4e superconductor, whose order parameter is reducible to the product of two Cooper pairs, and the latter as irreducible charge-4e superconductor with intrinsic quartetting. The topological properties of charge-4e superconductors have remained unexplored precisely because of their intrinsic correlation nature. Here we present the first systematic framework of topological charge-4e superconductors, combining explicit many-body wavefunctions with matching the edge conformal field theory and the bulk Chern-Simons topological quantum field theory. In particular, we find that the reducible topological charge-4e superconductors are at most fermionic SPTs, akin to the charge-2e chiral topological superconductor. On the other hand, the irreducible charge-4e superconductor can exhibit intrinsic topological order with deconfined anyons, and various nonabelian zero modes bound to superconducting vortices. Our results can be straightforwardly generalized to topological charge-2ne superconductors.