
TL;DR
This paper develops a mathematical framework to analyze objective moiré patterns with various symmetries, extending understanding beyond conventional layered materials and enabling applications in multiple scientific fields.
Contribution
It introduces an analytical approach for describing objective moiré patterns with different symmetries, broadening the scope of moiré pattern analysis beyond traditional layered structures.
Findings
Objective moiré patterns retain original symmetries with modified parameters.
Analytical descriptions for ring, 2D Bravais lattice, and helical patterns are derived.
Versatility demonstrated through conformal moiré patterns.
Abstract
Moir\'e patterns, typically formed by overlaying two layers of two-dimensional materials, exhibit an effective long-range periodicity that depends on the short-range periodicity of each layer and their spatial misalignment. Here, we study moir\'e patterns in objective structures with symmetries different from those in conventional patterns such as twisted bilayer graphene. Specifically, the mathematical descriptions for ring patterns, 2D Bravais lattice patterns, and helical patterns are derived analytically as representative examples of objective moir\'e patterns, using an augmented Fourier approach. Our findings reveal that the objective moir\'e patterns retain the symmetries of their original structures but with different parameters. In addition, we present a non-objective case, conformal moir\'e patterns, to demonstrate the versatility of this approach. We hope this geometric…
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Taxonomy
TopicsTopological Materials and Phenomena · Metamaterials and Metasurfaces Applications · Graphene research and applications
