Induced anomalous Hall effect of massive Dirac fermions in Zr Te 5 and Hf Te 5 thin flakes

Research on the anomalous Hall effect (AHE) has been lasting for a century to make clear the underlying physical mechanism. Generally, the AHE appears in magnetic materials, in which the extrinsic process related to scattering effects and intrinsic contribution connected with Berry curvature are crucial. Recently, AHE has been counterintuitively observed in nonmagnetic 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 $\mathrm{Zr}{\mathrm{Te}}_{5}$ and $\mathrm{Hf}{\mathrm{Te}}_{5}$ thin flakes in static ultrahigh magnetic fields up to 33 T. We find the AHE saturates to $55\phantom{\rule{0.16em}{0ex}}(70)\phantom{\rule{0.16em}{0ex}}{\mathrm{\ensuremath{\Omega}}}^{\text{}1}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\text{}1}$ for $\mathrm{Zr}{\mathrm{Te}}_{5}$ ($\mathrm{Hf}{\mathrm{Te}}_{5}$) thin flakes above $\ensuremath{\sim}10\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. 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 nonmagnetic topological materials $\mathrm{Zr}{\mathrm{Te}}_{5}$ and $\mathrm{Hf}{\mathrm{Te}}_{5}$ thin flakes. This model can identify our thin flake samples to be weak topological insulators and serve as a tool to probe the band structure topology in topological materials.