Disorder-induced topological superconductivity in a spherical quantum-Hall–superconductor hybrid

Quantum-Hall--superconductor hybrids have been predicted to exhibit various types of topological order, providing possible platforms for intrinsically fault-tolerant quantum computing. In this paper, we investigate disorder effects on the Rashba-coupled quantum-Hall system combined with the type-II superconductor. By diagonalizing the Bogoliubov--de Gennes Hamiltonian projected into a Rashba-coupled Landau level, we demonstrate the emergence of a topological superconducting phase resulting from disorders and proximity-induced pairing. Distinctive gapless modes appear in the real-space entanglement spectrum, which is consistent with topological superconductivity. Historically, the spherical geometry has been commonly used for identifying topologically ordered states, especially quantum-Hall physics, due to its compact and contractible nature. Motivated by this, we develop a formulation to construct this hybrid system on a sphere. Our numerical demonstrations are all performed on the spherical geometry.