Graphene Moire Superlattice Achieves 32% Nonlinear Hall Effect Via Lorentz Skew Scattering

The nonlinear Hall effect, a phenomenon with potential applications in energy harvesting and signal rectification, typically suffers from weak signals and inefficient control mechanisms. Pan He, Min Zhang, and Yue-Xin Huang, along with their colleagues, now report a significant advance in manipulating this effect, discovering a giant, field-tunable nonlinear Hall effect within a graphene moiré superlattice. The team demonstrates that this enhanced effect arises from a classical process called Lorentz skew scattering, induced by a perpendicular magnetic field, and exhibits a remarkably strong dependence on field strength and direction. Crucially, the observed nonlinear Hall conductivity reaches a record-high value, exceeding previously reported figures by over an order of magnitude, and establishes a new, efficient pathway for controlling Hall rectification in high-mobility materials.

Gate-Tuned Non-Linear Hall Effect in Moire Superlattices

Researchers have discovered a significant non-linear Hall effect in graphene-based moiré superlattices, a layered material structure engineered to create unique electronic properties. This effect, characterized by a substantial response to applied magnetic fields, is directly linked to the formation of secondary Dirac points within the superlattice structure, and demonstrates strong control through applied voltage. The team consistently observed this effect across multiple devices, confirming its intrinsic nature and potential for technological applications. The magnitude of the non-linear Hall effect changes predictably with applied gate voltage, allowing precise control over the material’s electronic properties.

Measurements reveal a proportional relationship between the effect and the strength of an applied magnetic field, and a dependence on the angle of the field itself. Detailed analysis confirms the effect’s quadratic dependence on electrical current, a hallmark of the non-linear Hall effect mechanism. Further investigations focused on understanding the underlying physics, revealing a connection between the non-linear Hall conductivity and the formation of secondary Dirac points. These points act as scattering centers for electrons, contributing to the observed non-linear response. The team also explored the relationship between non-linear and linear conductivity, discovering a strong correlation between the two. These findings provide insights into the fundamental physics of correlated electron systems and open possibilities for novel electronic devices based on moiré superlattices.

Giant Nonlinear Hall Effect via Lorentz Scattering

Scientists engineered a graphene-hBN moiré superlattice to investigate the non-linear Hall effect, and discovered a giant, field-tunable effect arising from Lorentz skew scattering. This process, where electrons are deflected by a magnetic field, provides a mechanism for controlling the effect with an external magnetic field, achieving a linear relationship between the effect’s magnitude and field strength. The team also observed a pronounced unidirectional angular dependence. To isolate the magnetic field-induced effect, the team conducted experiments at relatively low magnetic fields. Measurements confirmed a linear increase in the effect with increasing field strength, and a quadratic relationship with applied current, confirming its second-order nature.

The team also investigated the effect’s directional dependence by rotating the magnetic field, revealing a cosine-like relationship consistent with the vector nature of the Lorentz force in a two-dimensional system. Further analysis revealed a dominant quartic scaling relationship between non-linear and linear Hall conductivities, representing the highest power-law dependence observed to date and strongly supporting Lorentz skew scattering as the dominant mechanism. The team observed a giant non-linear Hall conductivity reaching up to 36000 μmV-1Ω-1, near van Hove singularities of the moiré minibands, and consistently reproduced these findings across multiple devices. Control devices lacking the aligned hBN structure exhibited negligible responses, confirming the critical role of the superlattice structure in generating this effect.

Giant Nonlinear Hall Effect in Graphene Moire Superlattices

Scientists have discovered a giant non-linear Hall effect in a graphene-hBN moiré superlattice, achieving a record-high non-linear Hall conductivity of 36000 μmV-1Ω-1. This breakthrough stems from a classical cooperative effect called Lorentz skew scattering, induced by an applied perpendicular magnetic field, and represents a significant advancement in energy harvesting and rectification technologies. Experiments reveal that the magnitude of this field-driven effect reaches up to 32% of the linear Hall signal, demonstrating a substantial increase in efficiency compared to previous methods. The team fabricated high-quality graphene devices encapsulated between layers of hexagonal boron nitride, creating a moiré superlattice with a period of approximately 14 nanometers.

This configuration breaks the graphene’s symmetry and generates unique electronic properties, including low-energy secondary Dirac points and van Hove singularities, which are crucial for enhancing the effect. Measurements of longitudinal and Hall resistance as a function of gate voltage confirm the reconstruction of the graphene band structure and the formation of these minibands. Researchers measured the second harmonic transverse voltage to probe the effect, carefully subtracting any zero-field contributions to isolate the magnetic field-driven effect. The observed effect exhibits a pronounced dependence on both gate voltage and magnetic field direction, changing sign with reversing the field.

Crucially, the magnitude of the effect varies linearly with magnetic field strength up to 0. 5 Tesla, and scales quadratically with the applied current, confirming its second-order nature. Further investigations revealed a unique unidirectional angular dependence of the effect, following a cosine-like relationship with the magnetic field orientation. Temperature-dependent measurements demonstrate a dramatic decrease in the effect with rising temperature, contrasting with the weak temperature dependence of the linear Hall effect, and highlighting the distinct physical origins of these phenomena. The team’s findings establish a new paradigm for achieving giant, tunable, and magnetically controlled effects in high-mobility quantum materials.

Giant Nonlinear Hall Effect in Graphene

This research demonstrates the discovery of a distinct type of non-linear Hall effect in graphene-hBN moiré superlattices, induced by applying a perpendicular magnetic field. The observed effect arises from a classical cooperative mechanism termed Lorentz skew scattering, and exhibits a linear dependence on the magnetic field strength, alongside a pronounced unidirectional angular dependence. Importantly, the magnitude of this field-driven effect reaches up to 32% of the linear Hall signal, representing a substantial advancement in the field. The team established a record-high non-linear Hall conductivity of 36000 μmV-1Ω-1, exceeding previously reported values by over an order of magnitude, and observed a unique quartic scaling law governing this effect.

This achievement is particularly notable as it occurs near van Hove singularities within the moiré minibands, highlighting the potential for tuning the effect through material properties. The ability to control this effect with an external magnetic field offers a broadly applicable paradigm for modulating the effect, moving beyond reliance on electrostatic gating. Future research directions include extending this magnetic-field-tunable effect to other two-dimensional materials, such as bilayer graphene and transition metal dichalcogenides, particularly those with flat electronic bands or strong correlation effects. The team also suggests that this mechanism may extend to non-linear thermal and thermoelectric Hall transports, and potentially to three-dimensional materials where electrostatic control is challenging.