—Study reveals unexpected quantum behavior between two and three dimensions
Scientists have discovered a previously unknown electronic phenomenon in a special form of ultrathin graphite, revealing that electrons may behave in fundamentally different ways when a material exists between two-dimensional and three-dimensional limits.
The research, recently published in the journal Nature, focused on a uniquely stacked form of graphene known as rhombohedral graphene. The material is composed of multiple graphene layers arranged in a staggered stacking sequence, with a total thickness of only a few nanometers. This study was jointly conducted by Associate Professor Liu Jianpeng’s team at the School of Physical Science and Technology (SPST), ShanghaiTech University, along with teams from Nanjing University and the Southern University of Science and Technology, among others.
At the center of the study is a phenomenon known as the anomalous Hall effect—a sideways deflection of electrons during electrical conduction.
Under normal conditions, electric current flows through a material in a straight line. When an external magnetic field is applied, however, electrons experience the Lorentz force and bend sideways, generating a transverse voltage. This is known as the Hall effect.
The anomalous Hall effect is more unusual. In this case, electrons can bend even without an external magnetic field, driven instead by the material’s own internal magnetism.
For many years, scientists generally believed that, in two-dimensional materials, such an effect could only occur if the material’s magnetization pointed perpendicular to the surface.
But the new experiments revealed something unexpected: in ultrathin rhombohedral graphene, electrons still exhibited strong sideways deflection even when the magnetization was primarily parallel to the material’s surface.
The observation suggests that electron behavior in this material is far more complex than previously understood.
According to the research team, the key lies in the material thickness being “just right.”
If the material consists of only one or two graphene layers, electrons are tightly confined within a two-dimensional plane. If it becomes too thick, however, the system behaves like ordinary three-dimensional graphite.
The graphene structures studied here are only a few nanometers thick—placing them precisely in between.
In this intermediate regime, electrons still move mostly within the plane, but the spatial region where they can exist—described in quantum mechanics by the electron wavefunction—begins to extend along the thickness direction. In other words, although electrons spend most of their time moving within the plane, they acquire a finite degree of three-dimensional freedom. The researchers believe that this additional freedom allows in-plane orbital magnetism—which would normally have little influence on electron motion in a purely two-dimensional system—to deflect electrons and generate a new type of anomalous Hall effect. Interestingly, such a quantum state with in-plane orbital magnetism exhibits a crescent-shaped Fermi surface, termed “Fermi lune” by the researchers.
The team named the phenomenon the “Transdimensional Anomalous Hall Effect.”
Here, “transdimensional” does not refer to science-fiction-like higher dimensions. Instead, it describes an electronic state that is neither fully two-dimensional nor conventionally three-dimensional, but exists in an intermediate regime between the two.
The significance of the discovery may not lie in an immediate technological application, but rather in opening a new direction in condensed matter physics.
For decades, scientists have largely treated two-dimensional and three-dimensional materials as fundamentally distinct systems. This work suggests that there may exist a previously underexplored “middle regime” between them, where electrons can display entirely new quantum behaviors.
Researchers believe the newly discovered mechanism could potentially provide new material platforms and physical concepts for:
magnetic memory technologies,
orbitronics devices that utilize electron orbital motion,
and future quantum information technologies.
More importantly, the work suggests that once materials are reduced to nanometer scales, “thickness” itself may become a new physical degree of freedom.