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Unconventional fermions with high degeneracies in three dimensions beyondWeyl and Dirac fermions have sparked tremendous interest in condensed matterphysics. Here, we study quantum Hall effects (QHEs) in a two-dimensional (2D)unconventional fermion system with a pair of gapped spin-1 fermions. We findthat the original unlimited number of zero energy Landau levels (LLs) in thegapless case develop into a series of bands, leading to a novel QHE phenomenonthat the Hall conductance first decreases (or increases) to zero and thenrevives as an infinite ladder of fine staircase when the Fermi surface is movedtoward zero energy, and it suddenly reverses with its sign being flipped due toa Van Hove singularity when the Fermi surface is moved across zero. We furtherinvestigate the peculiar QHEs in a dice model with a pair of spin-1 fermions,which agree well with the results of the continuous model.

Unconventional quantum Hall effects in two-dimensional massive spin-1 fermion systems