The Hall effect and its variations have been central to condensed-matter physics research. While the standard Hall effect and anomalous Hall effect require broken time-reversal symmetry (through magnetic fields or dopants), a second-order nonlinear Hall effect can exist in materials with time-reversal symmetry but lacking inversion symmetry. This effect stems from the Berry curvature dipole in momentum space. Previous studies have shown this effect in bilayer and multilayer WTe₂, Weyl semimetals, BiTeI under pressure, monolayer WTe₂ and MoTe₂ with an external electric field, and strained twisted bilayer graphene or WSe₂. Experimental observations have largely focused on 2D systems. The twist angle in 2D layered materials offers a control parameter to manipulate electronic structure, as seen in twisted bilayer graphene and transition metal dichalcogenides. This study investigates the nonlinear Hall effect in twisted bilayer WTe₂, utilizing first-principles calculations and a semiclassical approach, exploring twist angles from 12° to 73° to understand the role of the twist angle in modulating the nonlinear Hall effect.

The nonlinear Hall effect, arising from the Berry curvature dipole, has been a topic of significant recent research. Several materials have shown promise in exhibiting this effect, including Weyl semimetals, where the Berry curvature dipole is associated with Weyl points and their chiral anomaly. Other materials like BiTeI under pressure and monolayer transition metal dichalcogenides (TMDs) such as WTe₂ and MoTe₂ have also demonstrated the nonlinear Hall effect, often enhanced by external electric fields or strain. The application of strain to twisted bilayer graphene and WSe₂ has further amplified the observed nonlinear Hall response. This body of work motivates the investigation into twisted bilayer WTe₂, where the twist angle presents an additional degree of freedom for tuning electronic properties and potentially enhancing the nonlinear Hall effect.

The study employed first-principles calculations using the Vienna ab initio simulation package (VASP) with the projector-augmented wave (PAW) method. The generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) form was used for the exchange-correlation potential, with spin-orbit coupling included self-consistently. A plane-wave basis set with a 350 eV energy cutoff was used. A vacuum region exceeding 15 Å was applied to prevent interactions between the slab and its image. Structural optimization was performed until forces on each atom were less than 0.02 eV/Å. Van der Waals interactions were considered using the zero damping DFT-D3 method. Maximally localized Wannier functions were generated for the d orbitals of W and p orbitals of Te to compute Berry curvature and Berry curvature dipole. The first Brillouin zone was sampled using dense k-points to ensure convergence. The Berry curvature dipole was calculated using the formula derived from the semiclassical Boltzmann transport theory and the Berry curvature, which was calculated from the Wannier functions. The temperature dependence of Berry curvature dipole was calculated using the Fermi-Dirac distribution function.

The study constructed twisted bilayer WTe₂ structures with twist angles ranging from 12° to 73°. The optimized structures showed similar formation energies and average interlayer distances, slightly larger than in the perfect bilayer system. The twisted bilayer WTe₂ exhibited a more complex band structure compared to the perfect bilayer system, with abundant band anticrossings and inversions around the Fermi level, especially for θ = 29.4°. Analysis of the Berry curvature dipole (Dxz and Dyz) revealed a dramatic oscillating behavior near the Fermi level for θ = 29.4°, with Dxz reaching a peak of ~1400 Å. This is significantly larger than values reported in previous studies on monolayer or bilayer WTe₂, strained twisted bilayer WSe₂, strained twisted bilayer graphene, and artificially corrugated bilayer graphene. The analysis of band structure and Berry curvature distribution showed that the large Berry curvature dipole arises from the drastic change of Berry curvature in momentum space near the band edges. The temperature dependence of the Berry curvature dipole (Dyz) showed that for twisted bilayer WTe₂ (θ = 29.4°), it increases rapidly at temperatures below 20 K, suggesting a strong nonlinear Hall response at low temperatures. Similar large magnitude and oscillating behavior of the Berry curvature dipole were observed for θ = 40.1°, indicating a potential for giant nonlinear Hall effect across multiple twist angles.

The findings demonstrate that twisting bilayer WTe₂ significantly enhances the nonlinear Hall effect compared to its perfect bilayer counterpart. The observed giant Berry curvature dipole, exceeding previously reported values by orders of magnitude, is directly linked to the intricate band structure arising from the twist. The oscillating behavior of the nonlinear Hall response is a consequence of the complex Berry curvature distribution near the Fermi level, resulting from the numerous band anticrossings and inversions. The strong temperature dependence at low temperatures suggests that experimental observation of this giant nonlinear Hall effect is feasible. The tunability of the effect through the twist angle and Fermi level offers opportunities for controlling and manipulating the nonlinear Hall response. While the study focuses on the intrinsic contribution, extrinsic effects due to disorder in twisted bilayer systems (non-uniform twist angles) warrant further investigation.

This study predicts a giant nonlinear Hall effect in twisted bilayer WTe₂, attributed to the significantly enhanced Berry curvature dipole arising from the complex band structure induced by the twist. The large magnitude and tunability of the effect highlight twisted bilayer WTe₂ as a highly promising platform for studying nonlinear Hall physics. Future research should explore the influence of other twist angles, the role of disorder and other extrinsic effects, and the potential applications of this phenomenon in novel device technologies.

The study primarily focuses on the intrinsic contribution to the nonlinear Hall effect, neglecting potential extrinsic contributions from disorder, which could be significant in real twisted bilayer systems due to variations in the twist angle. The computational cost limited the analysis of a more comprehensive range of twist angles. Further experimental validation is necessary to confirm the predicted giant nonlinear Hall effect and its temperature dependence.