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Neutral edge modes in a superconductor -- topological-insulator hybrid structure in a perpendicular magnetic field

We study the low-energy edge states of a superconductor -- 3D topological-insulator hybrid structure (NS junction) in the presence of a perpendicular magnetic field. The hybridization of electron-like and hole-like Landau levels due to Andreev reflection gives rise to chiral edge states within each Landau level. We show that by changing the chemical potential of the superconductor, this junction can be placed in a regime where the sign of the effective charge of the edge state within the zeroth Landau level changes more than once resulting in neutral edge modes with a finite value of the guiding-center coordinate. We find that the appearance of these neutral edge modes is related to the level repulsion between the zeroth and the first Landau levels in the spectra. We also find that these neutral edge modes come in pairs, one in the zeroth Landau level and its corresponding pair in the first.