“Golden rules” for constructing atomic masses

The clock model shows the rotation alignment between the hour hand (top hBN), minute hand (middle graphene), and second hand (bottom hBN). The combination of the upper hBN, the middle graphene, and the lower hBn results in a super-rippled lattice structure in the center of the watch. Credit: National University of Singapore

Physicists have developed a technique to precisely align ultra-wavy lattices, revolutionizing the possibility of next-generation wavy quantum matter.

Physicists at the National University of Singapore (NUS) have developed a technique to precisely control the alignment of wavy superlattices using a set of golden rules, paving the way for the next generation of wavy quantum matter.

Supermoiré clamps

Moiré patterns are formed when two identical periodic structures are superimposed with a relative torsion angle between them or two different periodic structures but superimposed with or without a torsion angle between them. The torsion angle is the angle between the crystallographic orientations of the two structures. For example, when Graphene Hexagonal boron nitride (hBN) is a layered material layered on top of each other, and the atoms in the two structures don’t line up perfectly, creating a pattern of interference fringes, called a moiré pattern. This leads to electronic reconstruction.

The moiré pattern in graphene and hBN has been used to create new structures with exotic properties, such as topological currents and Hofstadter butterfly states. When two moiré patterns are stacked together, a new structure called a moiré mesh is created. Compared to traditional single corrugation materials, this super-corrugated network expands the range of tunable material properties allowing potential use in a much wider range of applications.

Achievements of the Department of Physics at NUS University

A research team led by Professor Ariando from the Department of Physics at the National University of Singapore has developed a technique and succeeded in achieving the controlled alignment of the hBN/graphene/hBN supermoiré network. This technique allows the precise arrangement of two moiré patterns, one on top of the other. Meanwhile, the researchers also formulated the “golden rule of three” to guide the use of their technique to create super-ripple networks.

The results were recently published in the journal Nature Communications.

Supermoiré mesh with twisted corners

Artistic illustration of the superlattice with twisted corners (θt and θb) formed between graphene and the top layer of hexagonal boron nitride (T-hBN) and the bottom layer of hexagonal boron nitride (B-hBN). A slight misalignment results in the formation of a super-wavy mesh pattern. Credit: Nature Communications

Challenges and solutions

There are three main challenges in creating the ultra-ripple graphene network. First, conventional optical alignment relies heavily on the straight edges of graphene, but finding a suitable graphene wafer is time-consuming and labor-intensive; Second, even if a graphene sample with straight edges is used, there is a low 1/8 probability of obtaining a double-aligned superripple lattice, due to the uncertainty of edge asymmetry and lattice symmetry. Third, although edge symmetry and mesh symmetry can be determined, alignment errors are often large (greater than 0.5°), as it is physically difficult to align two different mesh materials.

Dr. Junxiong Hu, lead author of the research paper, said: “Our technology helps solve a real-life problem. Several researchers have told me that it usually takes about a week to do the sample. With our technology, they can not only greatly shorten the manufacturing time, but also greatly improve Accuracy of the sample.”

Artistic insights

Scientists initially use a “30-degree rotation technique” to control the alignment of the top hBN and graphene layers. They then use an “inversion technique” to control the alignment of the upper hBN layers and the lower hBN layers. Based on these two methods, they can control the lattice symmetry and tune the band structure of the graphene superlattice. They also showed that an adjacent graphite edge can serve as a guide for stacking alignment. In this study, they fabricated 20 moiré samples with an accuracy of better than 0.2 degrees.

Professor Ariando said: “We have established three golden rules for our technology that can help many researchers in the 2D materials community. Our work is also expected to benefit many scientists working on other strongly interconnected systems such as magic-angle twisted bilayer graphene or ABC stacked multilayer graphene. Through this technical improvement, I hope it will accelerate the development of the next generation of wave quantum matter.

Future endeavours

Currently, the research team is leveraging this technology to fabricate a single-layer super-ripple graphene network and explore the unique properties of this material system. Moreover, they are also extending the current technique to other physical systems, to discover other new quantum phenomena.

Reference: “Controlled alignment of superwave lattice in doubly aligned graphene heterostructures” by Junxiong Hu, Junyou Tan, Mohamad M. Al Ezzi, Udvas Chattopadhyay, Jian Gou, Yuntian Zheng, Zihao Wang, Jiayu Chen, Reshmi Thottathil, Jiangbo Luo , Kenji Watanabe, Takashi Taniguchi, Andrew Thi Chien Wei, Shafik Adam and A. Ariando, July 12, 2023, Nature Communications.
doi: 10.1038/s41467-023-39893-5

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