Observation of Temperature Independent Anomalous Hall Effect in Thin Bismuth from Near Absolute Zero to 300 K Temperature

Technical Summary: Observation of a Temperature-Independent Anomalous Hall Effect in Thin Bismuth

Problem and Context
Elemental bismuth has long been the subject of studies due to its diamagnetism and semimetallic properties, which exhibit phenomena such as the Shubnikov–de Haas (SdH) effect and Nernst–Ettingshausen effects. While recent theoretical and experimental works have identified signatures of higher topology and superconductivity in bulk bismuth, the exploration of its two-dimensional (2D) form has been hindered by fabrication challenges. In contrast to graphite, the strong interlayer bonds of bismuth complicate mechanical exfoliation, restricting previous studies on thin bismuth (<100 nm) to molecular beam epitaxy (MBE) or nano-fabrication techniques. Furthermore, although an anomalous Hall effect (AHE) has been reported in bismuth fibers and bulk forms, the underlying mechanism remains unclear, particularly regarding the role of magnetic impurities versus intrinsic topological properties. A critical gap exists in understanding the electronic transport properties of single-crystal bismuth in the thin-film regime over a wide temperature range, specifically concerning the potential for a temperature-independent AHE, which is a hallmark of intrinsic mechanisms.

Methodology
The authors fabricated transport devices using a newly developed mechanical exfoliation technique based on micro-trench structures, enabling the production of thin bismuth flakes without MBE. A specific 68 nm thick van der Pauw (vdP) device was selected for detailed characterization. The device was coated with a PMMA layer to prevent oxidation and aging.

Transport measurements were performed in a perpendicular magnetic field ($B$) ranging from $\pm 30$ T and at temperatures from near absolute zero (15 mK in a dilution refrigerator; 1.4 K in a resistive magnet) up to 300 K. Due to the small size of the flake and the proximity of the ohmic contacts, the Hall resistance ($R_{xy}$) and the longitudinal resistance ($R_{xx}$) were inherently mixed. To decouple these signals, the authors applied Onsager's reciprocity theorem and measured resistance tensors with reversed current and voltage probes. The data were then symmetrized to extract the longitudinal resistance and antisymmetrized to extract the Hall resistance.

Main Results

1. Temperature-Independent AHE: The primary result is the observation of an anomalous Hall effect in the 68 nm thick bismuth device that is fully temperature-independent from 1.4 K to 300 K. Within experimental noise, the Hall resistance ($R_{xy}$) curves for all measured temperatures overlap perfectly, particularly in the low-field regime ($|B| < 2$ T). This behavior persists down to 15 mK.
2. Featureless Longitudinal Resistance: In stark contrast to the Hall signal, the longitudinal resistance ($R_{xx}$) exhibits temperature dependence consistent with semimetallic bismuth (resistance increases with temperature). However, the longitudinal magnetoresistance is entirely featureless across the entire range of $\pm 30$ T. There is no evidence of the $B^2$ scaling typical of semimetals, nor are SdH oscillations observed, which normally appear in bismuth at much lower fields (e.g., 1 T in bulk samples).
3. Intrinsic Mechanism: The authors analyze the scaling of the anomalous Hall conductivity ($\sigma_{AHE}$) against the longitudinal conductivity ($\sigma_{xx}$). The data follow the relationship $-\sigma_{AHE} \propto \sigma_{xx}^2$, which is characteristic of the intrinsic contribution to the AHE. This scaling, combined with the absence of temperature dependence, rules out extrinsic mechanisms such as skew scattering or side-jump, which rely on impurities and typically exhibit temperature dependence.
4. Absence of Magnetic Origin: Bismuth is a diamagnetic material and does not break time-reversal symmetry (TRS) in its bulk form. The authors confirm that the observed AHE is not due to magnetic impurities, as the effect persists without any magnetic order and the material's susceptibility is weak and temperature-dependent in a manner incompatible with ferromagnetism.

Significance and Claims
The work claims that the observation of a temperature-independent AHE in pure, non-magnetic bismuth is a significant and surprising result. The authors suggest that the mechanism is intrinsic and likely arises from a non-vanishing Berry curvature. While bulk bismuth preserves inversion symmetry (IS) and exhibits zero Berry curvature, theoretical calculations indicate that the surface of bismuth breaks IS and hosts a non-vanishing Berry curvature. The authors hypothesize that this surface Berry curvature, which does not require broken TRS, is responsible for the observed AHE.

The significance of this work lies in:

• Demonstrating that elemental bismuth, a well-studied semimetal, hosts a robust, temperature-independent AHE in the thin-film regime.
• Providing experimental evidence supporting the existence of surface-induced Berry curvature in bismuth.
• Proposing that bismuth could serve as a platform for exploring the quantum anomalous Hall effect (QAHE), as the intrinsic AHE is considered a precursor to the QAHE. The authors note that bismuth's buckled honeycomb lattice and high spin-orbit coupling are ingredients predicted by Haldane for the parity anomaly, opening the possibility of observing QAHE at higher temperatures than currently achieved in other systems.

The authors remain modest regarding the exact mechanism, noting that while surface Berry curvature is a plausible explanation, further theoretical and experimental work is required to identify the precise origin of the effect. They also point out that no existing model simultaneously explains the observed featureless longitudinal magnetoresistance and the temperature-independent AHE, suggesting that electronic transport in thin bismuth is not yet fully understood.