High-field Josephson effect enabled by a moiré Hofstadter spectrum

Magnetic fields generally suppress phase-coherent Josephson transport, limiting superconducting interferometry to relatively low fields. Here we show that moir\'e-engineered graphene Josephson junctions can overcome this constraint. Using ballistic graphene/hBN junctions, we establish phase-coherent Andreev transport through Fabry-P\'erot oscillations and Fraunhofer interference that persist across both the primary Dirac cone and reconstructed moir\'e minibands. We then demonstrate phase-coherent Josephson interference up to 6 T in the fractal Hofstadter-butterfly regime, well beyond the range expected for conventional ballistic graphene junctions. Comparison with Hofstadter-spectrum calculations reveals that superconductivity survives where the moir\'e potential transforms Landau levels with quenched group velocity into dispersive magnetic Bloch bands with finite quasiparticle group velocity, enabling extended electron-hole Andreev trajectories across the junction. Our results show that Hofstadter minibands can stabilize phase-coherent superconductivity deep into the parameter domain conventionally associated with the quantum Hall regime, establishing a new platform for high-field superconducting interferometry.