A Hierarchy of Topological and Superconducting States in Rhombohedral Hexalayer Graphene

Abstract: Superconductivity and the quantum Hall effect are conventionally viewed as mutually exclusive: the former is suppressed by magnetic fields, while the latter relies on them. Here, we report the surprising coexistence of these two phenomena in rhombohedral hexalayer graphene. In this system, a superconducting phase is not destroyed -- but instead stabilized -- by an out-of-plane magnetic field. Strikingly, this superconducting state coexists and competes with a sequence of quantum Hall states that appear at both integer and half-integer Landau level fillings. Both the superconducting and quantum Hall states exhibit sharply defined thermal transitions or crossovers, with nearly identical onset temperatures -- pointing to a shared underlying mechanism. Taken together, our observations uncover an unprecedented interplay between superconducting and topological phases, challenging conventional paradigms and opening a new frontier in condensed matter physics.