Observation of the nonlinear Hall effect under time reversal symmetric conditions (1809.09279v1)

Abstract: The electrical Hall effect is the production of a transverse voltage under an out-of-plane magnetic field. Historically, studies of the Hall effect have led to major breakthroughs including the discoveries of Berry curvature and the topological Chern invariants. In magnets, the internal magnetization allows Hall conductivity in the absence of external magnetic field. This anomalous Hall effect (AHE) has become an important tool to study quantum magnets. In nonmagnetic materials without external magnetic fields, the electrical Hall effect is rarely explored because of the constraint by time-reversal symmetry. However, strictly speaking, only the Hall effect in the linear response regime, i.e., the Hall voltage linearly proportional to the external electric field, identically vanishes due to time-reversal symmetry. The Hall effect in the nonlinear response regime, on the other hand, may not be subject to such symmetry constraints. Here, we report the observation of the nonlinear Hall effect (NLHE) in the electrical transport of the nonmagnetic 2D quantum material, bilayer WTe2. Specifically, flowing an electrical current in bilayer WTe2 leads to a nonlinear Hall voltage in the absence of magnetic field. The NLHE exhibits unusual properties sharply distinct from the AHE in metals: The NLHE shows a quadratic I-V characteristic; It strongly dominates the nonlinear longitudinal response, leading to a Hall angle of about 90 degree. We further show that the NLHE directly measures the "dipole moment" of the Berry curvature, which arises from layer-polarized Dirac fermions in bilayer WTe2. Our results demonstrate a new Hall effect and provide a powerful methodology to detect Berry curvature in a wide range of nonmagnetic quantum materials in an energy-resolved way.

• The paper demonstrates the first observation of a nonlinear Hall voltage in bilayer WTe2, challenging traditional time-reversal symmetry constraints.
• It employs dual-gated, encapsulated devices to reveal a quadratic voltage-current relationship and a Hall angle near 90°, linking the effect to Berry curvature dipoles.
• The study establishes a novel framework for probing quantum geometrical effects in nonmagnetic materials, paving the way for advancements in nonlinear transport applications.

Observation of the Nonlinear Hall Effect under Time Reversal Symmetric Conditions

The presented paper explores the nonlinear Hall effect (NLHE) in nonmagnetic materials, focusing on bilayer WTe$_2$, a two-dimensional quantum material. The authors report the observation of a nonlinear Hall voltage in bilayer WTe$_2$ in the absence of an external magnetic field. This research challenges the traditional constraints of time-reversal symmetry and extends our understanding of Hall effects within the nonlinear response regime.

Key Findings

The primary finding of this paper is the detection of a nonlinear Hall voltage that emerges when bilayer WTe$_2$ is subjected to an electric current. This discovery signifies that the second-order nonlinear Hall effect is prominent, differentiating itself from the classical and anomalous Hall effects, which typically align with linear electrical responses. The nonlinear Hall effect in WTe$_2$ demonstrates a quadratic voltage-to-current relationship and exhibits a Hall angle of approximately $90^\circ$, an unusual characteristic that sharply distinguishes it from metal-based anomalous Hall effects.

One of the most pivotal revelations from the paper is the relation of the NLHE to the Berry curvature dipole, which is derived from the Berry curvature distribution in momentum space. This dipole creates an electrical Hall effect even within the strictures of time-reversal symmetry, given that inversion symmetry is broken. In bilayer WTe$_2$, layer-polarized Dirac fermions emerge, leading to significant Berry curvature dipoles.

Experimental Approach

The researchers used dual-gated, encapsulated bilayer WTe$_2$ devices, enabling control over both charge density and out-of-plane electrical displacement fields. The materials were carefully fabricated to optimize measurement conditions, ensuring the detection of the anticipated nonlinear Hall voltages while maintaining low symmetry, crucial for observing significant Berry curvature effects.

Through systematic experimentation, including varied gate voltages and precise voltage measurements using a lock-in technique, the paper delineated not only the presence of the NLHE but also its dependence on electronic properties like the chemical potential and displacement field.

Theoretical Implications

The theoretical underpinning of this research situates the NLHE as a probe for Berry curvature distribution in nonmagnetic quantum materials. Previously, such effects were mainly explored and measured in magnetic materials due to alignment with the classical paradigm that requires time-reversal symmetry breaking. By illustrating a method to measure Berry curvature via electrical transport in materials where inversion symmetry is absent, this research posits an alternative way to explore the quantum metrics of novel materials.

The paper contributes a framework for understanding how intrinsic quantum properties can manifest in novel electrical phenomena. It hints at broader implications across electrical, thermoelectric, optical, and plasmonic domains and encourages further theoretical development to explore nonlinear transport effects arising from intrinsic quantum mechanics.

Conclusion and Future Directions

The authors effectively introduce a new category of Hall effect aligned with Berry curvature dipoles in nonmagnetic materials, proposing an innovative means to probe and understand quantum properties of materials with low symmetry, like WTe$_2$. The implications of this paper extend into potential practical applications, such as high-frequency devices, by exploiting the material's intrinsic quantum mechanical properties for nonlinear applications.

Future endeavors might explore the applicability of this phenomenon in other two-dimensional materials and diverse quantum systems, enabling a deeper comprehension and broader utility of quantum geometrical effects in electrical transport.