In a study published in Nature, scientists from Johns Hopkins University, the University of British Columbia, and the University of Washington have discovered a new class of quantum states in a specially designed graphene structure: topological electronic crystals in twisted bilayer–trilayer graphene, a system made by precisely rotating two-dimensional materials stacked one on top of the other.
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The starting point for this work is two flakes of graphene, which are made up of carbon atoms arranged in a honeycomb structure. The way electrons hop between the carbon atoms determines the electrical properties of the graphene, which ends up being superficially similar to more common conductors like copper.
Joshua Folk, Professor, Physics and Astronomy Department, University of British Columbia
“The next step is to stack the two flakes together with a tiny twist between them. This generates a geometric interference effect known as a moiré pattern: some regions of the stack have carbon atoms from the two flakes directly on top of each other, while other regions have the atoms offset,” added Folks.
He further added, “When electrons hop through this moiré pattern in the twisted stack, the electronic properties are totally changed. For example, the electrons slow way down, and sometimes they develop a twist in their motion, like the vortex in the water at the drain of a bathtub as it is draining out.”
The groundbreaking discovery revealed in this study was made by Ruiheng Su, an undergraduate student at UBC, while investigating a twisted graphene sample generated by Dr. Dacen Waters, a postdoctoral researcher in Prof. Matthew Yankowitz's group at the University of Washington.
Ruiheng discovered a new configuration for the device while working on the experiment at Folk's lab. The electrons in the graphene froze into a flawlessly ordered array, stuck in place but whirling in unison like ballet dancers gracefully performing stationary pirouettes. This synchronous rotation causes a fascinating phenomenon in which electric current flows smoothly along the sample's borders while the interior remains insulating due to electron immobilization.
The amount of current flowing along the edge is precisely defined by the ratio of two fundamental constants of nature: Planck’s constant and the electron's charge. This value's precision is assured by topology, a property of electron crystals that specifies the qualities of objects that remain intact even after minor deformations.
Just as a donut cannot be smoothly deformed into a pretzel without first cutting it open, the circulating channel of electrons around the boundary 2D electron crystal remains undisturbed by disorder in its surrounding environment.
Matthew Yankowitz, Professor, Department of Physics, University of Washington
“This leads to a paradoxical behavior of the topological electronic crystal not seen in conventional Wigner crystals of the past—despite the crystal forming upon freezing electrons into an ordered array, it can nevertheless conduct electricity along its boundaries,” stated Yankowitz.
The Möbius strip is a common example of topology—a simple yet mind-bending object. Consider taking a strip of paper, folding it into a loop, and taping the ends together. Now, grab another strip and twist it once before attaching the ends. The outcome is a Möbius strip, a surface with only one side and edge. No matter how one tries to manipulate the strip, untwisting it back into a normal loop without tearing it apart is impossible.
The rotation of the electrons in the crystal is analogous to the twist in the Möbius strip. It results in a remarkable feature of the topological electronic crystal that has never been seen before in the rare cases where electron crystals have been observed: edges where electrons flow without resistance, indicating that they are locked in place within the crystal.
The topological electron crystal is not only fascinating conceptually, but it also opens up new avenues for breakthroughs in quantum information. Future attempts to combine the topological electron crystal with superconductivity will provide the basis of qubits for topological quantum computers.
Journal Reference:
Su, R., et al. (2025) Moiré-driven topological electronic crystals in twisted graphene. Nature. doi.org/10.1038/s41586-024-08239-6