标题： 石墨烯薄膜中的跨维度异常霍尔效应 显示英文标题

标题： Transdimensional anomalous Hall effect in rhombohedral thin graphite

摘要： 异常霍尔效应（AHE）出现在时间反演对称性被打破的材料中，体现了磁有序和电子轨道运动之间复杂的相互作用[1-4]。 在二维（2D）系统中，AHE总是与垂直于平面的轨道磁化耦合，这种耦合与面内手性轨道运动有关。 在三维（3D）系统中，载流子可以在第三维方向上沿着垂直的平均自由程lz隧穿或散射。 当样品厚度远大于lz时，散射会破坏相干的垂直运动，使得3D AHE本质上成为一个厚度平均的2D对应物[4]——仍然由面内的轨道运动产生的垂直轨道磁化所支配。 在这里，我们探索了一个未被探索的区域，在这个区域中，样品厚度远大于原子层厚度，但小于或与lz相当。 在这种“跨维度”区域中，载流子能够在二维平面内及之外维持相干的轨道运动，从而导致一种根本上新的AHE类型，该类型同时耦合了垂直和面内的轨道磁化。 我们报告了在静电门控菱形九层石墨烯中首次观察到这种现象——跨维度AHE（TDAHE）。 这种状态源自一种特殊的金属相，该相自发地打破了时间反演、镜像和旋转对称性，这是由电子-电子相互作用驱动的。 这种TDAHE表现为同时出现的垂直和面内霍尔电阻滞后，受沿任一方向的外部磁场控制。 我们的发现揭示了一类新的AHE，为跨维度系统的关联和拓扑物理开辟了一个未被探索的范式。 显示英文摘要

摘要： Anomalous Hall effect (AHE), occurring in materials with broken time-reversal symmetry, epitomizes the intricate interplay between magnetic order and orbital motions of electrons[1-4]. In two dimensional (2D) systems, AHE is always coupled with out-of-plane orbital magnetization associated in-plane chiral orbital motions. In three dimensional (3D) systems, carriers can tunnel or scatter along the third dimension within the vertical mean free path lz. When sample thickness far exceeds lz, scattering disrupts coherent out-of-plane motion, making 3D AHE effectively a thickness-averaged 2D counterpart[4] -- still governed by out-of-plane orbital magnetization arising from in-plane orbital motions. Here, we explore an uncharted regime where the sample thickness is much larger than the atomic layer thickness yet smaller than or comparable to lz. In such "transdimensional" regime, carriers can sustain coherent orbital motions both within and out of the 2D plane, leading to a fundamentally new type of AHE that couples both out-of-plane and in-plane orbital magnetizations. We report the first observation of such phenomenon -- transdimensional AHE (TDAHE) -- in electrostatically gated rhombohedral ennealayer graphene. This state emerges from a peculiar metallic phase that spontaneously breaks time-reversal, mirror and rotational symmetries driven by electron-electron interactions. Such TDAHE manifests as concurrent out-of-plane and in-plane Hall resistance hysteresis, controlled by external magnetic fields along either direction. Our findings unveils a new class of AHE, opening an unexplored paradigm for correlated and topological physics in transdimensional systems.