[Paper Review] Induced anomalous Hall effect of massive Dirac fermions in ZrTe5 and HfTe5 thin flakes

Yanzhao Liu, Huichao Wang+9 more|arXiv (Cornell University)|Dec 15, 2020

Topological Materials and Phenomena7 references4 citations

TL;DR

This study demonstrates that the anomalous Hall effect (AHE) in non-magnetic ZrTe5 and HfTe5 thin flakes arises from the splitting of massive Dirac bands—without Weyl points—under high magnetic fields. The AHE saturates at 55 (ZrTe5) and 70 (HfTe5) ohm⁻¹·cm⁻¹ above 10 T, with Berry curvature calculations confirming a weak topological insulator state, offering a new probe for band topology in topological materials.

ABSTRACT

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.

Motivation & Objective

• To resolve the contradiction between observed AHE saturation in experiments and theoretical predictions based on Weyl point scenarios in non-magnetic topological materials.
• To investigate the origin of the anomalous Hall effect in ZrTe5 and HfTe5 thin flakes under ultrahigh magnetic fields (up to 33 T).
• To determine whether massive Dirac fermions with band splitting can account for the observed AHE without requiring Weyl points.
• To establish a new method for probing band structure topology in topological materials using the AHE response.
• To clarify the topological nature of ZrTe5 and HfTe5 thin flakes through combined magnetotransport and Berry curvature analysis.

Proposed method

• Conducted magnetotransport measurements on exfoliated ZrTe5 and HfTe5 thin flakes under static ultrahigh magnetic fields up to 33 T.
• Performed detailed Hall resistance and longitudinal resistivity measurements to extract the anomalous Hall conductivity.
• Calculated the Berry curvature from first-principles electronic structure calculations to link band topology to AHE response.
• Analyzed the band structure to identify massive Dirac fermions with spin-splitting that break inversion symmetry.
• Used the observed saturation of AHE at high fields (above 10 T) as a key constraint to rule out Weyl point-based mechanisms.
• Correlated experimental AHE magnitude with theoretical Berry curvature to confirm the origin of the effect.

Experimental results

Research questions

• RQ1 Can the anomalous Hall effect in non-magnetic ZrTe5 and HfTe5 thin flakes be explained without invoking Weyl points?
• RQ2 What is the origin of the observed saturation of the anomalous Hall effect at high magnetic fields (~10 T) in these materials?
• RQ3 How does the splitting of massive Dirac bands contribute to the anomalous Hall effect in the absence of intrinsic magnetism?
• RQ4 To what extent can the anomalous Hall effect serve as a probe for the topological nature of the band structure in these materials?
• RQ5 Is the observed AHE consistent with a weak topological insulator phase in ZrTe5 and HfTe5?

Key findings

• The anomalous Hall effect in ZrTe5 and HfTe5 thin flakes saturates at 55 and 70 ohm⁻¹·cm⁻¹, respectively, above 10 T, indicating a robust, field-independent contribution.
• The saturation behavior contradicts predictions from Weyl point models, which would predict unsaturated AHE even at high fields.
• Berry curvature calculations reveal that the splitting of massive Dirac bands—without Weyl points—generates a significant intrinsic contribution to the AHE.
• The observed AHE is attributed to the intrinsic mechanism driven by nontrivial Berry curvature from spin-split massive Dirac fermions.
• The results identify ZrTe5 and HfTe5 thin flakes as weak topological insulators, with the AHE serving as a direct probe of their band topology.
• The study establishes a new method to probe topological band structures in non-magnetic materials using the Hall effect, independent of magnetic order.