Spin and orbital mixing of edge states in a quantum Hall system proximitized by a superconductor

We investigate the formation and transport properties of chiral Andreev edge states in a two-dimensional quantum Hall system proximitized by a superconductor. By numerically modeling the system using the Bogoliubov-de Gennes equations, we analyze the non-local conductance and transmission probabilities of multimode and spinful systems. We demonstrate that the Andreev reflection process induces a mixing of the quantum Hall edge modes at higher filling factors, a phenomenon strictly prohibited in clean, purely electronic systems. When incorporating the Zeeman interaction, we show that the Andreev edge states split into uncoupled spin species, maintaining spin orthogonality that prevents mixing between opposite spin sectors. Furthermore, we explore the impact of Rashba spin-orbit coupling. While the spin-orbit interaction alone causes slight spin depolarization, its combination with an in-plane magnetic field drives complex spin mixing among all chiral Andreev bands, fundamentally altering the conductance oscillations. Finally, we reveal that the electron transmission probabilities exhibit robust degeneracies, which emerge as a direct consequence of the unitarity constraints and the particle-hole symmetry of the system's scattering matrix in a magnetic field and the presence of spin-orbit interaction.