Nine-layer graphene reveals quantum state that defies century of physics

Pesquisadores of Universidade of Nanjing, in China, led by Lei Wang and Geliang Yu, observed for the first time completely new electronic behavior that contradicts principles established over a hundred years ago. The phenomenon, called the “Hall Anômalo Transdimensional Effect” (TDAHE), was detected in rhombohedral graphene with a thickness of just 2 to 5 nanometers. The discovery represents a fundamental advance in understanding how electrons behave on microscopic scales and opens up prospects for ultra-low power memory devices.

The law that governed electronic physics for more than a century

Durante generations, physics established a rule considered absolute: the “Law of Ortogonalidade”. Esse principle determines that three fundamental components — magnetization (M), current flow (J) and resulting electric field (E_H) — must always be perpendicular to each other. The rule worked perfectly in known systems, shaping all scientific understanding of the behavior of electrons in magnetic fields.

#NJU Joint Research Published in Nature

Recently, the research group led by Professor Lei Wang at the School of Physics, Nanjing University, in collaboration with Professor Geliang Yu’s group at Nanjing University, Associate Professor Jianpeng Liu’s group at ShanghaiTech… pic.twitter.com/DO7kzMmekR

— Nanjing University (@NJU1902) April 30, 2026

In two-dimensional systems, such as a single layer of graphene, electrons move in a plane, with magnetization oriented perpendicularly. Nos dense three-dimensional systems, electrons gain freedom of vertical movement, but frequently collide with impurities, nullifying any coherent orbital movement. The resulting behavior always converged to the sum of the two-dimensional cases. Teoricamente, some researchers had already proposed the existence of states capable of circumventing this fundamental law, but achieving this in real materials presented gigantic challenges for decades.

Rhombohedral Grafeno as an environment for the transdimensional phenomenon

The material chosen for this experiment was not accidental. Rhombohedral Grafeno with a very specific thickness — just a few atomic layers of carbon — created the perfect environment for observing transdimensional behavior. Nessa tiny scale, electrons find an unexplored domain where the rules of both dimensions do not strictly apply.

The theoretical challenge was formidable. Graphene, composed exclusively of carbon, has a property called “spin-orbit interaction” that is extremely weak, with a magnitude of approximately 40 μeV. Essa interaction links the rotation and orbit of electrons. Pesquisadores believed that it was impossible to achieve an anomalous Hall effect with in-plane magnetization in graphene systems, as this property was considered essential in heavy metallic elements. The current discovery completely overturns this theoretical limitation.

The mechanism of transdimensional electronic dance

The explanation of the phenomenon involves sophisticated concepts of quantum physics, but reveals a remarkable elegance. The researchers elucidated how electronic waves undergo crescent-shaped distortions. Essa deformation results from an intense repulsive force between the electrons themselves, not depending on the exclusive spin-orbit interaction of heavy metals as previously supposed.

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In the new transdimensional state, the in-plane and out-of-plane orbital magnetizations couple simultaneously in a coherent manner. Electrons maintain two-dimensional planar motion while performing three-dimensional vertical motion at the same time. Esse simultaneous coupling violates the Lei of Ortogonalidade that would prevail in any other known context. The team observed the effect through careful measurements of Hall’s current, magnetization, and voltage, revealing a completely new geometric relationship.

• Observado in rhombohedral graphene with a thickness of 2 to 5 nanometers.
• Magnetizações coupled orbitals simultaneously in-plane and out-of-plane.
• Viola to Lei from Ortogonalidade established over a hundred years ago.
• Não depends on spin-orbit interaction of heavy metals.
• Promete applications in ultra-low power magnetic memory.

Aplicações technologies in memory and data storage

The importance of this discovery extends far beyond academic interest. Pure orbital magnetism, manifested without dependence on spin-orbit interaction of heavy metals, provides a new design principle for innovative devices. Pesquisadores already points to the promise of ultra-low power magnetic memory, a critical technology for the era of artificial intelligence.

Dispositivos conventional memory devices consume significant amounts of power when writing and retrieving data. A mechanism based on the transdimensional anomalous Hall effect could perform these operations with dramatically reduced power dissipation. Além Furthermore, the discovery opens doors for exploring other exotic quantum states that may exist in similar material structures, expanding the possibilities for technological innovation in the coming years.

Redefinindo the boundaries between dimensions in modern physics

The discovery highlights a profound reality: human understanding of nature has been shaped by lived experience in three dimensions. Cientistas drew clear boundaries between the extremely thin two-dimensional world exemplified by graphene and the three-dimensional world where we live. The behavior of electrons has been classified into one of these two categories, and all of modern condensed matter physics has been built on these foundations.

But nature has proven to be more sophisticated than our categories. Nos spaces of just a few nanometers between extremely thin layers of carbon, a hitherto unexplored realm exists. Nessa dimensional gap, the laws of both dimensions do not apply exactly. The behavior of electrons follows neither the 2D planar model nor the 3D volumetric model, but represents something genuinely new that challenges centuries of established understanding.