Unified topological phase diagram of quantum Hall and superconducting vortex-lattice states

We present the global topological phase diagram of a two-dimensional electron gas placed in a quantizing magnetic field and proximitized by a superconducting vortex lattice. Our theory allows for arbitrary ratios of the pairing amplitude, magnetic field, and chemical potential. By analyzing the Bogoliubov--de Gennes Hamiltonian, we show that the resulting phase diagram is highly nontrivial, featuring a plethora of topological superconducting phases with chiral edge modes of quasiparticles. Landau-level mixing plays an essential role in our theory: even in the weak-pairing limit, it generically splits the integer quantum Hall transition lines into a sequence of transitions with larger Chern number jumps of both signs protected by the symmetries of the superconducting vortex lattice. Interestingly, we find that weak pairing induces trivial or topological superconductivity when chemical potential is tuned to a Landau level energy, depending on the Landau level index.