Patterns of Patterns: Exploring Supermoiré Engineering

Key takeaways

• An interference pattern that emerges from three stacked and twisted layers of graphene, called a supermoiré pattern, can uncover hidden properties of simpler moiré materials.
• SEAS physicists used a highly specialized microscope to show how supermoiré patterns influence the material’s properties.
• Controlling the structural imperfections introduced by supermoiré patterns could help researchers design next-generation materials.

A few years ago, physicists were surprised to learn that stacking and subtly twisting two atomically thin layers of an electronic material like graphene creates a pattern that changes the material’s properties and can even turn it into a superconductor. This superimposed grid, like what would emerge if two window screens were laid slightly askew, is called a moiré pattern.

But why stop there? It turns out adding a third layer, with each layer twisted at slightly different angles, produces even more complex interferences known as supermoiré patterns (a.k.a. moiré of moiré). The supermoiré pattern induces profound changes in how electrons move through the material, but until recently, scientists had had trouble measuring exactly what changes occur and why.

Now, applied physicists in the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) have used a specially designed microscope to probe the properties of supermoiré patterns in trilayer graphene to an extent that was never possible before. Using their microscope, they saw many new states of matter in which electrons would get stuck or form unusual groups, leading to changes in the entire system’s electronic behavior and opening doors to studying layered materials with precisely controllable properties.  

Research challenges assumptions about moiré structures

Published in Science, the research was co-led by former Harvard Quantum Initiative Prize postdoctoral fellow Yonglong Xie and former SEAS graduate student Andrew Pierce, who worked in the lab of Amir Yacoby, the Mallinckrodt Professor of Physics and Applied Physics.

The ultra-long supermoiré patterns visible in twisted trilayer materials had been considered by some to be imperfections of little consequence amidst the simpler moiré structures that emerge when only two layers are present. The new Harvard paper challenges that assumption and introduces the concept of supermoiré engineering – how that additional pattern-on-pattern could be used as a probe to uncover the overall properties of these special materials. The supermoiré pattern is relatively large and can be easily controlled, introducing potential for designing exotic new materials for thin electronics and other applications.

“Going into this study, if you asked me if I thought the supermoiré was good for anything, I probably would’ve said it’ll just be a nuisance,” said Pierce, now a postdoctoral researcher at Cornell. “But it turned out to give us new information about the system – information that would’ve been hard to get with other techniques besides ours.”

Microscope with nanometer resolution

Understanding of supermoiré patterns had been limited by the fact that the patterns can vary significantly across different regions in a sample. To solve this problem, the researchers used their single-electron transistor microscope, developed in Yacoby’s lab at SEAS, that’s capable of examining materials with spatial resolution of about 100 nanometers and is sensitive to perturbations in individual electrons. A sharp needle with a sensor at its tip scans the sample and captures these details.

The microscope allowed the team to detect very slight changes in moiré and supermoiré patterns in two- and -three-layer graphene, and the resulting electronic properties per pixel. By analyzing the correlations between these quantities, they gleaned new insights into how the supermoiré patterns in particular influence the entire system.

“This additional long-range pattern that until now was largely overlooked could be used as a probe to understand the material properties of the parent material,” said Xie, now an assistant professor at Rice University.

The results could enhance understanding of quantum phenomena, including the lossless conduction of electrons known as superconductivity, and lead to next-generation materials that contain multiple tunable properties.

The paper was co-authored by Jeong Min Park, Daniel E. Parker, Jie Wang, Patrick Ledwith, Zhuozhen Cai, Kenji Watanabe, Takashi Taniguchi, Eslam Khalaf, Ashvin Vishwanath, and Pablo Jarillo-Herrero. The research received federal support from the Army Research Office, the National Science Foundation, and the Department of Defense.