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

Quantum-Hall--Superconductor hybrids have been predicted to exhibit varioustypes of topological order, providing possible platforms for intrinsicallyfault-tolerant quantum computing. In this paper, we develop a formulation toconstruct this hybrid system on a sphere, a useful geometry for identifyingtopologically ordered states due to its compact and contractible nature. As apreliminary step using this framework, we investigate disorder effects on theRashba-coupled quantum Hall system combined with the type-II superconductor. Bydiagonalizing the BdG Hamiltonian projected into a Rashba-coupled Landau level,we demonstrate the emergence of a topological superconducting phase resultingfrom disorders and proximity-induced pairing. Distinctive gapless modes appearin the real-space entanglement spectrum, which is consistent with topologicalsuperconductivity.