Theoretical physicist discovers how twisting a material’s layers can generate a mysterious effect that bends the path of electrons

In 2018, a discovery in materials science caused shock waves throughout the community. A team has shown that stacking two layers of graphene – a honeycomb-shaped layer of carbon extracted from graphite – at a precise “magic angle”, turns it into a superconductor, says Ritesh Agarwal of the University from Pennsylvania.

This gave rise to the field of “twistronics,” revealing that twisting materials in layers could unlock extraordinary material properties.

Building on this concept, Agarwal, Penn theoretical physicist Eugene Mele, and their collaborators took twistronics into new territories.

In a study published in Naturethey studied spirally stacked tungsten disulfide (WS₂) and discovered that by twisting these layers, light could be used to manipulate electrons. The result is analogous to the Coriolis force, which bends the trajectories of objects in a rotating frame, like the behavior of wind and ocean currents on Earth.

“What we found was that by simply twisting the material, we could control how the electrons moved,” says Agarwal, a Srinivasa Ramanujan Distinguished Research Fellow in the School of Engineering and Applied Sciences. This phenomenon was particularly evident when the team shone circularly polarized light onto WS.₂ spirals, causing electrons to deflect in different directions depending on the internal twist of the material.

The origins of the team’s latest findings date back to the early days of the COVID-19 pandemic lockdowns, when the lab was closed and first author Zhurun ​​(Judy) Ji was completing her doctorate.

Unable to conduct physical experiments in space, she focused on more theoretical work and collaborated with Mele, the Christopher H. Browne Distinguished Professor of Physics in the School of Arts and Sciences.

Together, they developed a theoretical model of how electrons behave in twisted environments, based on the hypothesis that a continually twisted lattice would create a strange and complex landscape in which electrons could exhibit new quantum behaviors.

“The structure of these materials is reminiscent of DNA or a spiral staircase. This means that the usual rules of periodicity in a crystal, where atoms form neat, repeating patterns, no longer apply,” explains Ji.

As 2021 arrived and pandemic restrictions were lifted, Agarwal learned at a scientific conference that his former colleague Song Jin at the University of Wisconsin-Madison was growing crystals with a continuous spiral twist. Recognizing that Jin’s spiral twisted WS₂ The crystals were the perfect material to test Ji and Mele’s theories, so Agarwal arranged for Jin to send a batch. The experimental results were intriguing.

Mele says the effect reflects the Coriolis force, an observation that is usually associated with the mysterious lateral deviations seen in rotating systems. Mathematically, this force looks a lot like a magnetic deflection, explaining why electrons behaved as if a magnetic field was present even when one wasn’t there. This discovery was crucial because it linked the twisting of the crystal and the interaction with circularly polarized light.

Agarwal and Mele compare the electronic response to the classic Hall effect in which current flowing through a conductor is deflected laterally by a magnetic field. But, while the Hall effect is driven by a magnetic field, here “the twisting structure and Coriolis-like force guided the electrons,” says Mele.

“The discovery wasn’t just about finding this force; it was about understanding when and why it appears and, more importantly, when it shouldn’t appear.”

One of the major challenges, Mele adds, was that once they recognized that this Coriolis deviation could occur in a twisted crystal, it seemed like the idea worked too well. The effect appeared so naturally in theory that it seemed difficult to turn it off, even in scenarios where it shouldn’t exist. It took almost a year to establish the exact conditions under which this phenomenon could be observed or suppressed.

Agarwal compares the behavior of electrons in these materials to “going down a slide in a water park.” If an electron went down a straight slide, like conventional material lattices, everything would be smooth. But, if you sent him down a spiral slide, it’s a completely different experience. The electron feels forces pushing it in different directions and emerges changed, almost as if it were a little “dizzy”.

This “dizziness” is particularly exciting for the team because it introduces a new degree of control over the movement of electrons, achieved only through the geometric twisting of the material. Additionally, the work also revealed strong optical nonlinearity, meaning the material’s response to light was significantly amplified.

“In typical materials, optical nonlinearity is weak,” says Agarwal, “but in our twisted system it is remarkably strong, suggesting potential applications in photonic devices and sensors.”

Another aspect of the study concerned moiré patterns, which are the result of a slight angular misalignment between layers that plays a significant role in the effect. In this system, the length scale of moiré, created by twisting, is comparable to the wavelength of light, allowing light to interact strongly with the structure of the material.

“This interaction between light and the moiré pattern adds a layer of complexity that enhances the effects we observe,” says Agarwal, “and this coupling is what allows light to control the behavior of electrons so effectively.”

When light interacted with the twisted structure, the team observed complex wave functions and behaviors not observed in classical two-dimensional materials. This result is linked to the concept of “higher order quantum geometric quantities”, such as Berry curvature multipoles, which provide insight into the quantum states and behaviors of the material.

These results suggest that twisting fundamentally changes the electronic structure, creating new pathways to control electron flow in ways that traditional materials cannot.

And finally, the study found that by slightly adjusting the thickness and workability of the WS₂ spirals, they could refine the strength of the optical Hall effect. This tunability suggests that these twisted structures could provide a powerful tool for designing new quantum materials with highly tunable properties.

“We have always been limited in how we can manipulate the behavior of electrons in materials. What we have shown here is that by controlling twist we can introduce completely new properties,” says Agarwal.

“We are only scratching the surface of what is possible. With the spiral structure providing a new way for photons and electrons to interact, we are entering into something completely new. What more can this system reveal ?”