Spectral asymmetry induces a re-entrant quantum Hall effect in a topological insulator

The band inversion of topological materials in three spatial dimensions is intimately connected to the parity anomaly of two-dimensional massless Dirac fermions. At finite magnetic fields, the parity anomaly reveals itself as a non-zero spectral asymmetry, i.e., a non-zero difference between the number of conduction and valence band Landau levels, due to the unpaired zero Landau level. Here, we realize this two-dimensional Dirac physics at a single surface of the three-dimensional topological insulator (Hg,Mn)Te. We observe an unconventional re-entrant quantum Hall effect that can be directly related to the occurrence of spectral asymmetry in a single topological surface state. The effect should be observable in any topological insulator where the transport is dominated by a single Dirac surface state.