A Hierarchy of Superconductivity and Topological Charge Density Wave States in Rhombohedral Graphene

Superconductivity and the quantum Hall effect are conventionally regarded as mutually exclusive: superconductivity is suppressed by magnetic fields, whereas the quantum Hall effect relies on them. Here we report a striking exception, where an unconventional superconducting phase is stabilized by an out-of-plane magnetic field and coexists with a re-entrant integer quantum Hall (RIQH) effect in moiré-less rhombohedral hexalayer graphene. The re-entrant quantum Hall state, arising from a bubble-like charge density wave (CDW), provides a natural backdrop for the emergence of superconductivity. Angle-resolved transport reveals that the field-stabilized superconducting phase occupies the same density--displacement-field regime as a stripe-ordered phase at zero field, yet only develops once the stripe is replaced by a bubble-like CDW at finite field. These findings demonstrate a decisive role of CDW order in stabilizing superconductivity in rhombohedral graphene, establishing a new paradigm for the interplay between superconductivity and quantum Hall physics.