Topologically enabled superconductivity and rhombohedral tetralayer graphene

We present a topological mechanism for superconductivity emerging from Chern-2 insulators. While, naively, time reversal symmetry breaking is expected to prevent superconductivity it turns out that the opposite is the case: An explicit model calculation for a generalized attractive-U Haldane-Hubbard model demonstrates that superconductivity is only stabilized near the quantum anomalous Hall state, but not near a trivial, time reversal symmetrical band insulator. We explain this using an effective fractionalized field theory involving fermionic chargons, bosonic colorons and an emergent U(1) gauge field. When chargons form a topological band structure, they prevent monopole proliferation ensuring a gapless photon. We argue that this photon should be interpreted as the Goldstone boson of the superfluid. Using random phase approximation on top of extensive slave-rotor mean-field calculations we characterize coherence length and stiffness of the superconductor. Thereby, we deduce the phase diagram in parameter space along with the universal nature of the superconducting transitions. We furthermore discuss the effect of doping and external magnetic field. We complement the fractionalized theory with calculations using an effective spin model and Gutzwiller projected wavefunctions. While mostly based on a simple toy model, we argue that our findings pave the way to a better understanding of superconductivity emerging out of spin- and valley polarized tetralayer rhombohedral graphene in a parameter regime with nearby quantum anomalous Hall insulators.