Heterostructures of superconductors and quantum-Hall insulators are promising platforms for topological quantum computation. However, these two systems are incompatible in some aspects, such as a strong magnetic field, the Meissner effect, and chirality. In this work, we address the condition that the superconducting proximity effect works in the bulk of quantum Hall states, and identify an essential role played by the vortex lattice regardless of pairing symmetry. We extend this finding to a heterostructure between a chiral $p$-wave superconductor in the mixed state and an integer quantum Hall insulator. The proximity effect works selectively in the lowest Landau level, depending on relative chiralities. If the chiralities align, a topological phase transition to a topological superconductor occurs.

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• Integer quantum Hall effect
• Proximity effect
• Topological superconductors
• Vortex lattices