Transdimensional anomalous Hall effect in rhombohedral thin graphite

TL;DR

This paper reports the discovery of a new type of anomalous Hall effect in rhombohedral multilayer graphene, where carriers exhibit coherent orbital motions both within and out of the 2D plane, revealing a transdimensional AHE driven by electron interactions.

Contribution

It introduces the concept of transdimensional AHE, observed in a novel regime where sample thickness is comparable to the mean free path, and demonstrates this effect in rhombohedral multilayer graphene.

Findings

Observation of concurrent out-of-plane and in-plane Hall resistance hysteresis.

Identification of a metallic phase breaking multiple symmetries.

Control of AHE via external magnetic fields.

Abstract

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.