  Researches on anomalous Hall effect (AHE) have been lasting for a century to
make clear the underlying physical mechanism. Generally, the AHE appears in
magnetic materials, in which extrinsic process related to scattering effects
and intrinsic contribution connected with Berry curvature are crucial.
Recently, AHE has been counterintuitively observed in non-magnetic topological
materials and attributed to the existence of Weyl points. However, the Weyl
point scenario would lead to unsaturated AHE even in large magnetic fields and
contradicts the saturation of AHE in several tesla (T) in experiments. In this
work, we investigate the Hall effect of ZrTe5 and HfTe5 thin flakes in static
ultrahigh magnetic fields up to 33 T. We find the AHE saturates to 55 (70)
Ohm^-1*cm^-1 for ZrTe5 (HfTe5) thin flakes above ~ 10 T. Combining detailed
magnetotransport experiments and Berry curvature calculations, we clarify that
the splitting of massive Dirac bands without Weyl points can be responsible for
AHE in non-magnetic topological materials ZrTe5 and HfTe5 thin flakes. This
model can identify our thin flake samples to be weak topological insulators and
serve as a new tool to probe the band structure topology in topological
materials.
