The flat world

A 2D material is a crystal so thin that it is only one or a few atoms thick – a sheet rather than a lump. Most come from layered crystals of the kind met in Level 1: strong bonds inside each layer, a weak van der Waals attraction between the layers. Take one layer from the stack and you have a monolayer; two make a bilayer, and a handful a few-layer flake.

Graphene is the famous example: one honeycomb sheet of carbon atoms, taken from graphite. But it is one of hundreds. Boron nitride makes a honeycomb sheet too, of boron and nitrogen. Molybdenum disulfide, MoS₂, makes a sandwich three atoms thick: a sheet of molybdenum between two sheets of sulfur. Each behaves differently, and each changes when it is thinned to a single layer.

‘Two-dimensional’ does not mean the sheet has no thickness – nothing real is that thin. It means the sheet is so thin that its electrons can move only sideways, within the plane, and that every one of its atoms sits at a surface. Both facts change almost everything about how the material behaves.

The word is sometimes stretched. Flakes tens of layers thick are often sold, and even published, as ‘2D’, though they behave much like the bulk crystal. A real 2D material is defined by a measured thickness, not by its label.

For most of the twentieth century, physicists thought a crystal one atom thick could not survive on its own: heat would make it crumple or fall apart. Layered crystals had been split into thin flakes for decades, and single layers had even been made chemically, but nobody had a simple way to isolate one and measure it as an electronic device.

In 2004, Andre Geim and Konstantin Novoselov at the University of Manchester did it with ordinary sticky tape. They pressed tape onto a piece of graphite, peeled it off, and peeled the flakes apart again and again, thinning them each time. Then they pressed the tape onto a silicon wafer coated with a thin glassy layer – and under an ordinary microscope the thinnest flakes, a single atom thick, showed up as a faint but visible tint, through the same effect that colours a soap bubble.

They went further: they made the flakes into tiny electrical devices and showed that a voltage could change how well graphene conducts. That paper started the field. A year later the same simple method gave single layers of boron nitride, MoS₂ and others, showing that graphene was the first of a large family. In 2010 Geim and Novoselov shared the Nobel Prize in Physics.

Sticky tape still gives the best flakes for research. It cannot make them in quantity, though, and Level 5 covers the methods that can.

A single layer is not just a very thin piece of the bulk crystal. Several things change at once when a crystal is thinned to one layer – the Basics page explains eight – and four matter most at this stage.

There is no inside. Every atom of a monolayer is a surface atom, so whatever touches it – the surface below, molecules from the air, a voltage on a nearby electrode – acts on the whole material at once. That makes 2D materials superb sensors, and very easy to spoil.

Squeezing the electrons changes their energy. Confined to a sheet, electrons can only take certain energies, and the band gap shifts. MoS₂ is the striking case: as a bulk crystal it gives off almost no light, but as a single layer it glows brightly, because thinning changes the kind of gap it has.

Electrons stop hiding from each other. In a thick crystal, the material around two charges weakens their pull on each other. In a single layer there is almost nothing around them, so an electron and the gap it leaves behind bind into a tight pair, an exciton, which then decides how the layer takes in and gives out light.

New knobs appear. A voltage, a stretch or a twist between two stacked layers can change what the material is, not just how it is packaged. Two layers of graphene twisted by about 1.1 degrees become a superconductor near absolute zero.

Graphene was first, but the family is now large, and it covers almost every kind of behaviour known in solids. Flatland’s catalogue groups the members by the kind of crystal they come from.

Graphene behaves almost like a metal: electricity flows easily, but it has no band gap, so it cannot be switched off. Hexagonal boron nitride, hBN, is its insulating twin – the same honeycomb, made of boron and nitrogen, with a wide gap – and it is the standard protective layer in research devices. The transition metal dichalcogenides, TMDCs, such as MoS₂ and WSe₂, include semiconductors that switch and glow, as well as metals and superconductors. MXenes, made by etching one element out of a bulk crystal, are metallic sheets used in coatings, batteries and electromagnetic shielding. Xenes such as silicene are single-element sheets like graphene but made of other elements, and most of them are fragile in air. Some layers are magnets: CrI₃ stays magnetic even as a single layer.

Not every sheet called 2D is two-dimensional in the same way. Some are peeled from layered crystals; some exist only as layers grown on a support; some are thin flakes made in liquids. The catalogue marks each family with what kind of sheet it really is – the first thing to check before believing a claim about it.

It is easy to read about graphene ‘revolutionising’ something every week, so it is worth being precise about what is real. Most of what is sold today uses 2D materials in bulk – as an additive or a coating – rather than as a single perfect layer.

Graphene and related flakes are sold by the tonne as additives in composites, coatings and sports equipment. Thin graphite and graphene films spread heat sideways in phones, where there is no room for a fan. Small amounts help the electrodes of batteries conduct, and some supercapacitors use them for their huge surface area. The first sensors in which a 2D material is the active part, detecting gases or molecules in medical tests, are on the market.

Devices built on a single perfect layer are still mostly in laboratories and pilot lines. Chip makers are developing transistors with channels of MoS₂ and WSe₂ for future generations of chips, photodetectors and optical chips are being tested, and stranger physics, such as superconductivity in twisted layers, has no product in sight.

Flatland sorts every application by how close it is to something you can buy, from ‘shipping now’ to ‘speculative’. Keeping that scale in mind is the best defence against hype: a laboratory result is the start of a long road, not a product.

Some beliefs about 2D materials are common enough to be worth tackling head on. The Basics page lists ten; four come up most often.

‘Graphene will replace silicon.’ Not in the switches of a computer chip: graphene has no band gap, so it cannot be turned fully off. Its future in electronics lies alongside silicon, and 2D materials with a gap, such as MoS₂, are the candidates for transistors.

‘One atom thick must mean fragile.’ A perfect sheet of graphene is the strongest material ever measured. Thinness makes it easy to bend, and easy to tear from a flaw – which is why real sheets, with their defects and edges, fall far short of the textbook number.

‘If a product says it contains graphene, it does.’ A 2018 study of material from 60 producers found that most were selling flakes of graphite many layers thick, not graphene. A measured layer count, not a label, is the test.

‘2D materials were discovered in 2004.’ Very thin layers had been made since the 1960s, and single layers of MoS₂ were made chemically in 1986. What 2004 brought was a simple method anyone could repeat, and proof that a single layer works as an electronic device – which is why the field took off then.

Holding on to these corrections is the real outcome of this level: you can now tell the honest version of the story to someone else.