How can electrons can split into fractions of themselves?

MIT physicists have taken a key step toward solving the puzzle of what leads electrons to split into fractions of themselves. Their solution sheds light on the conditions that give rise to exotic electronic states in graphene and other two-dimensional systems.

The new work is an effort to make sense of a discovery that was reported earlier this year by a different group of physicists at MIT, led by Assistant Professor Long Ju. Ju’s team found that electrons appear to exhibit “fractional charge” in pentalayer graphene — a configuration of five graphene layers that are stacked atop a similarly structured sheet of boron nitride.

Ju discovered that when he sent an electric current through the pentalayer structure, the electrons seemed to pass through as fractions of their total charge, even in the absence of a magnetic field. Scientists had already shown that electrons can split into fractions under a very strong magnetic field, in what is known as the fractional quantum Hall effect. Ju’s work was the first to find that this effect was possible in graphene without a magnetic field — which until recently was not expected to exhibit such an effect.

The phenemonon was coined the “fractional quantum anomalous Hall effect,” and theorists have been keen to find an explanation for how fractional charge can emerge from pentalayer graphene.

The new study, led by MIT professor of physics Senthil Todadri, provides a crucial piece of the answer. Through calculations of quantum mechanical interactions, he and his colleagues show that the electrons form a sort of crystal structure, the properties of which are ideal for fractions of electrons to emerge.

“This is a completely new mechanism, meaning in the decades-long history, people have never had a system go toward these kinds of fractional electron phenomena,” Todadri says. “It’s really exciting because it makes possible all kinds of new experiments that previously one could only dream about.”

The team’s study appeared last week in the journal Physical Review Letters. Two other research teams — one from Johns Hopkins University, and the other from Harvard University, the University of California at Berkeley, and Lawrence Berkeley National Laboratory  — have each published similar results in the same issue. The MIT team includes Zhihuan Dong PhD ’24 and former postdoc Adarsh Patri.

“Fractional phenomena”

In 2018, MIT professor of physics Pablo Jarillo-Herrero and his colleagues were the first to observe that new electronic behavior could emerge from stacking and twisting two sheets of graphene. Each layer of graphene is as thin as a single atom and structured in a chicken-wire lattice of hexagonal carbon atoms. By stacking two sheets at a very specific angle to each other, he found that the resulting interference, or moiré pattern, induced unexpected phenomena such as both superconducting and insulating properties in the same material. This “magic-angle graphene,” as it was soon coined, ignited a new field known as twistronics, the study of electronic behavior in twisted, two-dimensional materials.

“Shortly after his experiments, we realized these moiré systems would be ideal platforms in general to find the kinds of conditions that enable these fractional electron phases to emerge,” says Todadri, who collaborated with Jarillo-Herrero on a study that same year to show that, in theory, such twisted systems could exhibit fractional charge without a magnetic field. “We were advocating these as the best systems to look for these kinds of fractional phenomena,” he says.

Then, in September of 2023, Todadri hopped on a Zoom call with Ju, who was familiar with Todari’s theoretical work and had kept in touch with him through Ju’s own experimental work.

“He called me on a Saturday and showed me the data in which he saw these [electron] fractions in pentalayer graphene,” Todadri recalls. “And that was a big surprise because it didn’t play out the way we thought.”

In his 2018 paper, Todadri predicted that fractional charge should emerge from a precursor phase characterized by a particular twisting of the electron wavefunction. Broadly speaking, he theorized that an electron’s quantum properties should have a certain twisting, or degree to which it can be manipulated without changing its inherent structure. This winding, he predicted, should increase with the number of graphene layers added to a given moiré structure.

“For pentalayer graphene, we thought the wavefunction would wind around five times, and that would be a precursor for electron fractions,” Todadri says. “But he did his experiments and discovered that it does wind around, but only once. That then raised this big question: How should we think about whatever we are seeing?”

Extraordinary crystal

In the team’s new study, Todadri went back to work out how electron fractions could emerge from pentalayer graphene if not through the path he initially predicted. The physicists looked through their original hypothesis and realized they may have missed a key ingredient.

“The standard strategy in the field when figuring out what’s happening in any electronic system is to treat electrons as independent actors, and from that, figure out their topology, or winding,” Todadri explains. “But from Long’s experiments, we knew this approximation must be incorrect.”

While in most materials, electrons have plenty of space to repel each other and zing about as independent agents, the particles are much more confined in two-dimensional structures such as pentalayer graphene. In such tight quarters, the team realized that electrons should also be forced to interact, behaving according to their quantum correlations in addition to their natural repulsion. When the physicists added interelectron interactions to their theory, they found it correctly predicted the winding that Ju observed for pentalayer graphene.

Once they had a theoretical prediction that matched with observations, the team could work from this prediction to identify a mechanism by which pentalayer graphene gave rise to fractional charge.

They found that the moiré arrangement of pentalayer graphene, in which each lattice-like layer of carbon atoms is arranged atop the other and on top of the boron-nitride, induces a weak electrical potential. When electrons pass through this potential, they form a sort of crystal, or a periodic formation, that confines the electrons and forces them to interact through their quantum correlations. This electron tug-of-war creates a sort of cloud of possible physical states for each electron, which interacts with every other electron cloud in the crystal, in a wavefunction, or a pattern of quantum correlations, that gives the winding that should set the stage for electrons to split into fractions of themselves.

“This crystal has a whole set of unusual properties that are different from ordinary crystals, and leads to many fascinating questions for future research,” Todadri says. “For the short term, this mechanism provides the theoretical foundation for understanding the observations of fractions of electrons in pentalayer graphene and for predicting other systems with similar physics.”

This work was supported, in part, by the National Science Foundation and the Simons Foundation. 

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