Moiré Patterns with Atoms
What is a moiré pattern?
The word moiré comes from French textiles, where layered fabrics created beautiful rippling patterns. Artists and designers have used these effects for centuries — and scientists noticed something exciting: the same patterns appear when simple shapes or grids are placed on top of each other slightly out of line.
This is a great example of how art, design, and science inspire each other — patterns that look decorative can also reveal deep scientific ideas.
Have I seen moiré patterns before?
You have probably seen moiré patterns before, whenever similar patterns are overlayed then shifted or rotated compared to each other. The created visual effect is called large-scale wave interference. You can notice this:
- When looking through two fences, grids or window screens behind each other, creating various patterns.
- When trying to take a photo of an LCD screen with your phone, coloured ripples appear on the picture.
- Patterned materials, like a striped shirt or bird feathers can appear to be rippled in digital photos or seem to wave and pulse if moving in videos.
Maths behind moiré patterns
When two repeating patterns overlap at a slightly different angle or with slightly different spacing and create a moiré pattern, mathematical equations can predict:
- the size of the new pattern,
- how it changes rotation and spacing.
Moiré patterns in atomic systems
Some materials, like graphene (a single layer of carbon atoms arranged in a honeycomb pattern), are only one atom thick. If you place two such layers on top of each other and rotate one slightly, a moiré pattern appears! This isn’t just beautiful — but changes the properties of the material in exciting ways!
As the layers are rotated, some atoms will be directly above another atom in the second layer, and so be close to each other, while others will be slightly further apart. These tiny changes can dramatically alter how the material behaves: how well it conducts electricity, whether it becomes superconducting (carrying electricity with no energy loss) or if it displays any of the wide range of exotic quantum states.
These properties can be observed not only in graphene, but in other layered materials as well, like boron-nitride (also a honeycomb structure, but boron and nitrogen atoms at the vertices of the hexagons rather than carbons) or transition metal dichalcogenides (for example WS2 or MoSe2, forming more complex layered structures, but still resembling the honeycomb arrangement if looking from above).
However, synthesising layered materials with a specific angle of relative rotation is challenging. To understand and predict the properties of these materials, for example finding so called “magic angles” where certain behaviour is observed, computational modelling has to be used. Using physics-based models, it becomes possible to accurately calculate the behaviour of these layered materials, testing different rotational angles, compositions and even include the effects of external conditions like temperature. Such simulations can help design smarter materials for quantum technologies and more efficient electronic devices.
Our HetSys PhD student, Anas Siddiqui has been studying Moiré patterns in layered 2D materials.
All the instructions and printable patterns are in the PDF below. Just download it, follow the steps, and start experimenting.
Try changing the angle, spacing, or direction of the patterns to see what new effects you can create. There’s no single “right” answer—this activity is all about exploring and having fun with patterns and movement.
Tip :Once you’ve made your model, show it to friends or family and see what patterns they discover!