MIT physicists have made a significant breakthrough in understanding the phenomenon where electrons split into fractions of their usual charge, offering new insights into the behaviour of exotic electronic states in graphene and other two-dimensional materials.
This latest research builds on a discovery earlier this year, when a team led by Assistant Professor Long Ju at MIT reported that electrons in pentalayer graphene—a structure composed of five graphene layers stacked on top of boron nitride—exhibited fractional charge. Remarkably, this behaviour was observed without the application of a magnetic field, challenging prior assumptions.
Previously, scientists knew that under a strong magnetic field, electrons could split into fractions as part of the fractional quantum Hall effect. However, Ju’s findings marked the first time such fractional behaviour occurred in graphene without any magnetic influence, which led to the coining of the “fractional quantum anomalous Hall effect.” Since then, researchers have been eager to uncover how fractional charge could emerge in this unusual system.
MIT professor Senthil Todadri, who led the new study published in Physical Review Letters, offers a critical piece of the puzzle. Through detailed quantum mechanical calculations, Todadri and his team discovered that the electrons in pentalayer graphene form a crystal-like structure, which provides the ideal conditions for fractional electron behavior.
“This is a completely new mechanism,” said Todadri. “In the decades-long history of studying these phenomena, no one has observed a system that naturally leads to such fractional electron effects. It opens the door to all kinds of new experimental possibilities.”
The study, which includes contributions from Zhihuan Dong and former postdoc Adarsh Patri, is part of a wider body of research. Two other teams—one from Johns Hopkins University and another from Harvard University, UC Berkeley, and Lawrence Berkeley National Laboratory—have also reported similar findings in the same journal issue.
Building on “Twistronics” and the Magic-Angle Graphene Discovery
This research builds upon the work of MIT physicist Pablo Jarillo-Herrero and his team, who in 2018 were the first to demonstrate that twisting two sheets of graphene could give rise to novel electronic behaviors. This discovery of “magic-angle graphene” spurred a new field known as “twistronics,” focused on understanding how the interactions between twisted two-dimensional materials could lead to unusual quantum phenomena, such as superconductivity and insulating behavior.
“We quickly realized that these twisted systems could provide the right conditions for fractional electron phenomena to emerge,” said Todadri, who collaborated with Jarillo-Herrero on a 2018 study that theorized such systems might exhibit fractional charge without a magnetic field. “We saw these systems as ideal platforms to study these fractional effects.”
A Surprising Discovery and the New Crystal Model
In September 2023, Todadri received an unexpected call from Ju, who was eager to share data showing fractional charge behavior in pentalayer graphene. This discovery caught Todadri by surprise, as it did not align with his earlier predictions. In his 2018 paper, Todadri had theorized that fractional charge would emerge from a specific twisting of the electron wavefunction, and that this twisting would intensify as more graphene layers were added.
“Initially, we expected the wavefunction to wind five times in pentalayer graphene,” Todadri explained. “But Ju’s experiments showed that it only wound once. This raised a big question—how do we explain what we’re seeing?”
Uncovering the Electron “Crystal”
Todadri and his team revisited their hypothesis and discovered they had overlooked an important factor. The conventional approach in the field had been to treat electrons as independent entities and analyze their quantum properties. However, in the confined, two-dimensional space of pentalayer graphene, electrons are forced to interact with each other, behaving according to their quantum correlations in addition to their natural repulsion.
By incorporating these interelectron interactions into their model, the team was able to match their predictions with the experimental data Ju had obtained. This led them to a crucial realization: the moiré pattern formed by the stacked graphene layers induces a weak electrical potential that forces the electrons to interact and form a crystal-like structure. This electron “crystal” creates a complex pattern of quantum correlations, allowing for the formation of fractional charge.
“The crystal has a whole set of unique properties that differentiate it from ordinary crystals,” said Todadri. “This opens up many exciting avenues for future research. In the short term, our work provides a theoretical foundation for understanding the fractional electron observations in pentalayer graphene and predicting similar phenomena in other systems.”
This new insight paves the way for further exploration into how graphene and other two-dimensional materials might be used to engineer new electronic states, with potential applications in quantum computing and other advanced technologies.