AI 中文总结
本研究预测了非磁性或反铁磁双层体系中存在层非线性霍尔效应，揭示其层奇宇称特性与多种产生机制，通过对称性分析和第一性原理计算验证了该效应的电可调性，为非线性输运研究提供新方向。
AI 中文摘要
非线性霍尔效应为研究固体中的量子几何提供了有力工具，并且能够实现突破线性响应限制的整流现象。在本快报中，我们预测在由线性霍尔电导率为零的非磁性或反铁磁材料构成的堆叠双层体系中，存在一种“层非线性霍尔效应（layer nonlinear Hall effect, LNHE）”。在此类体系中，二阶或三阶非线性霍尔响应本质上具有层奇宇称性：两个组成层的贡献大小相等但符号相反，在层交换对称性下会完全抵消。面外电场$E_z$可以打破这种对称性，从而揭示隐藏的响应并将其转化为可切换的宏观非线性霍尔信号。利用最小$k\bm{\cdot}p$模型，我们证明LNHE可源于贝里曲率偶极子机制。通过对全部80个层群的系统对称性分析，我们进一步得到了允许此类LNHE存在的对称性约束和堆叠构型的完整分类。除该机制外，额外的对称性分析表明LNHE也可能由量子度量偶极子或逆质量偶极子产生。值得注意的是，即使在二阶非线性霍尔响应被对称性禁止的情况下，三阶LNHE仍可在某些堆叠双层构型中存在。对代表性双层材料——非磁性1T$'$-WTe$_2$和1T$'$-ReS$_2$——的第一性原理计算明确证实了电可逆的二阶LNHE，与我们基于对称性的预测完全一致。总体而言，我们的研究结果确立了LNHE是广泛层状量子材料中的普遍现象，并为实现电可调非线性输运提供了可靠途径。
英文摘要
Nonlinear Hall effects provide a powerful probe of quantum geometry in solids and enable rectification phenomena beyond the constraints of linear response. In this Letter, we predict a \emph{layer nonlinear Hall effect} (LNHE) in stacked bilayer systems composed of nonmagnetic or antiferromagnetic materials with a vanishing linear Hall conductivity. In such systems, the second- or third-order nonlinear Hall responses are intrinsically layer odd: the contributions from the two constituent layers have equal magnitude but opposite sign, resulting in exact cancellation under layer-exchange symmetry. An out-of-plane electric field $E_z$ can break this symmetry, thereby unveiling the hidden response and converting it into a switchable macroscopic nonlinear Hall signal. Using a minimal $k\!\cdot\!p$ model, we demonstrate that the LNHE can originate from the Berry curvature dipole mechanism. A systematic symmetry analysis of all 80 layer groups further yields a complete classification of the symmetry constraints and stacking configurations that allow for this type of LNHE. Beyond this mechanism, additional symmetry analysis reveals that LNHE may also arise from quantum metric dipole or inversed mass dipole. Remarkably, even in cases where second-order nonlinear Hall responses are symmetry forbidden, a third-order LNHE can still survive in certain stacked bilayer configurations. First-principles calculations on representative bilayers---nonmagnetic 1T$'$-WTe$_2$ and 1T$'$-ReS$_2$---explicitly demonstrate electrically reversible second-order LNHE, in full agreement with our symmetry-based predictions. Overall, our results establish LNHE as a universal phenomenon in a wide range of layered quantum materials and provide a robust route toward electrically tunable nonlinear transport.
