  The recent experimental observations of the quantum Hall effect in 3D
topological semimetals have attracted great attention, but there are still
debates on its origin. We systematically study the dependence of the quantum
Hall effect in topological semimetals on the thickness, Fermi energy, and
growth direction, taking into account the contributions from the Fermi-arc
surface states, confinement-induced bulk subbands, and helical side-surface
edge states. In particular, we focus on the intensively studied Dirac semimetal
Cd$_{3}$As$_{2}$ and its slabs grown along experimentally accessible
directions, including [001], [110], and [112]. We reveal an ignored mechanism
from the Zeeman splitting of the helical edge states, which along with
Fermi-arc 3D quantum Hall effect, may give a non-monotonic dependence of the
Hall conductance plateaus on the magnetic field in the most experimentally
studied [112] direction slab. Our results will be insightful for exploring the
quantum Hall effects beyond two dimensions.
