EVERYTHING is made of atoms. To understand this, we’re asked to imagine that the smooth continuous materials around us are each made up of tiny lumps. 

Rather than acting like little inert building bricks, each is humming with the energy of existing. Every atom is itself an immense void with even tinier positive and negative charged matter suspended in space, whizzing round each other and changing configuration to give the atom its own particular properties. 

The dynamism of the charges moving around and interacting both inside the atom and outside of it defines the ways that charge and energy can move between them, through space, sometimes joining them together in configurations of molecules of infinite variety. 

Some of the details have changed, but much of this imagined interior world of matter has been with us since antiquity. 

It should be easy, apparently, to accept — that despite the fact we can never experience the atoms, viscerally with our eyes, or feel them — they are nevertheless real. The smallest thing we might be able to see, with good enough eyes, would be about the size of a wavelength of light (or several wavelengths) which is the minimum size that (our imperfect eyes notwithstanding) it could be physically possible to see. 

Atoms are ten thousand times smaller than that. As such, we’ll never see them, except indirectly by using scientific tools to measure their presence. 

Imagining these atoms is for many of us very difficult, and perhaps a bit pointless, but it is doing this and picturing the ways that atoms connect to each other that forms the basis of the whole discipline of chemistry, and increasingly material science too.

Rather than thinking about chunks of bulk material, many material scientists are now interested in imagining materials on this scale. 

They do this in order to understand the properties of the atoms themselves, much of which are incredibly complex and unknown, but also in order to build new materials from the most fundamental scale with unusual properties. 

One particularly popular sort of material in recent years might even help us imagine the atomic scale for ourselves. These materials are tangible and macroscale in two dimensions, but only 2D, being just one atom thick. 

Atoms arranged in materials like this induce a symmetry in one another that prevents them curling up into the third dimension to make lumps, they instead flatten out into a stable, ultra-thin sheet. 

Astonishing as it seems when imagined from the point of view of a fizzing, empty atom, or from the normal 3D world, these materials are not particularly rare. In the world of 2D materials, all the normal rules apply, except now flattened out into just two directions. This produces some weird effects. 

This two dimensionality can also increase the control that we have over some physical processes. 

Depending on the material and how we use it, electricity can be conducted, light can be emitted and all from materials of the thinnest possible width. If, that is, we can work out how to make it, and manipulate it.

Graphene is the most famous of these materials. Graphene is a sheet of pure carbon, each carbon embedded in a neat geometrical honeycomb lattice, strongly bound into the flat sheet. 

In graphite, which we use in pencils, these layers are stacked on top of each other, bonded fairly loosely. Graphene received a particular popularity boost just over a decade ago when researchers in Manchester showed that you can extract truly atom-thick graphene layers from lumps of graphite, or even from a pencil scribble, just using sticky tape. 

The layers themselves are very tough with atoms tightly connected, but because they are loosely stacked on top of each other, sellotape glue is enough to lift one layer off the layer below. (Getting it off the sellotape is a lot harder! You have to dissolve the sellotape.)

This result astounded nanophysicists and engineers, who are well aware of how difficult it is to make or manipulate 2D materials — growing, extracting or holding onto the atom-thick materials can be understandably tricky. 

Even since the revelation of the simple sticky tape trick, there has still been lots of difficulty in making large and uniform enough graphene sheets to be able to use systematically in technological applications and enjoy the benefits of 2D in sensors and electronics. 

Much research work is ongoing into inventing new manufacturing techniques to make the incorporation of 2D materials into our everyday lives a reality. In the meantime, other scientists still work with graphene sheets and other 2D materials to discover fundamental properties of atom-thick materials. 

Because it’s so hard to make high-quality graphene, they often work by making tiny randomly shaped fragments of the material, which must be identified and manipulated by hand under microscopes. It’s fiddly work connecting them up into electrical circuits under different conditions to explore their internal structures.

One interesting idea is carefully controlling the restacking of the atom-thick sheets in different configurations. Because the sheets are so perfectly arranged according to the symmetry of the constituent atoms, they are highly geometrical. 

This means that by arranging these sheets on top of each other, interactions between these flattened atoms can be carefully reorganised and tested to understand what happens at each precise orientation. 

For example, scientists are interested in what happens in materials in which each layer is at a slight angle with the sheet below, making an unusual twisted screw of material, which might change the way that the materials interact with light or charge. 

People trying to understand this phenomenon have made careful studies by laboriously moving pieces of graphene into position on top of each other by hand. 

However, at the end of October some scientists in the US reported in Science that they’ve thought of a new way to get just this effect by making stacks of 2D material crystals with a specifically designed twist. Even better, the technique uses crystal growth to produce the geometrical effect, eliminating the need for arrangement by hand.

The idea is very simple: you simply let the layers of the 2D material grow out (crystallise) sideways in both of the two dimensions of their spatial extent. 

Instead of growing the crystals on a flat surface, you grow them on bumps (the researchers call the bumps carefully controlled, although you can imagine that at this scale it might be a hazard of the job that you get a few random bumps). 

The 2D sheets grow flat over part of the surface bump, but the unevenness of the surface means that as the material adds extra area, it grows round and over the top of itself like a collapsed spiral staircase. Depending on the size and shape of the bump on which the crystal is grown, the angle round which the 2D layer turns is different, meaning that it can potentially be controlled, creating different alignments of spiralling sheets.

These little stacks of spiral materials turn a 2D layer into a 3D rotating stack. 

Just as the reorientation of a strip of paper in three dimensions creates the mysterious möbius strip, these spirals create an exotic geometry, very different from a normal flat plane, and unlike any materials that have been grown and exploited in the lab before. 

Imagining the atoms in these materials means thinking of the snaking levels of a multi-storey car-park, each layer just one atom thick, with charges moving across the surface, up and down the different levels. 

Understanding how movement of charges and energy occurs on these structures means that we can understand more about the way that abstract geometries interact with real-life materials. 

We don’t know what might be possible if the shape could be scaled up to make bulk, tangible materials with the same internal structure.

For now, the materials that these researchers made are tiny scraps of matter, made of only a few thousand atoms, and therefore not visible outside of a microscope themselves. 

Although researchers say that the spiral geometries are controllable, there is no direct intention to use the materials in a practical application at this stage. 

Still, inside these tiny crystals we’ve seen for the first time a new world of helter-skelter 2D materials, and it might lead anywhere.