a two-dimensional material
A ream of paper is a stack of sheets: each sheet is strong and continuous in its own plane, but the sheets slide over one another and peel apart with almost no effort. Some crystals are built exactly like that — layers held tightly within each layer by strong chemical bonds, but stacked on their neighbours only by weak van der Waals forces. Peel one sheet off such a crystal and you have a two-dimensional material: a sheet of atoms one, or a few, atoms thick that is nonetheless a proper crystal in its plane. Graphene, a single layer of graphite, is the founding example.
In graphene the carbon atoms sit at the corners of a honeycomb — a repeating pattern of hexagons — held by strong covalent bonds about 0.142 nm long, so a single sheet is remarkably stiff and strong even though it is just one atom thick. Its cousins share the layered idea with different chemistry: hexagonal boron nitride is a honeycomb of alternating boron and nitrogen, an electrical insulator; the transition-metal dichalcogenides such as molybdenum disulphide are three-atom-thick sandwich layers. All were long known as bulk layered solids; the shift to two-dimensional materials came in 2004 when single graphene sheets were first isolated and shown to survive on their own.
Thinning a layered crystal to a single sheet does more than make it small — it changes the structure's consequences. Molybdenum disulphide, an ordinary semiconductor in bulk, becomes a direct-gap light emitter as a monolayer; graphene's electrons behave as if massless. And because the sheets are held together so weakly, they can be re-stacked at will — graphene on boron nitride on a dichalcogenide — into van der Waals heterostructures that mix and match properties layer by layer, a Lego set for structure at the ultimate thinness.
The original graphene was made by pressing sticky tape onto a lump of graphite and peeling: the weak van der Waals bonds between layers give way first, lifting off flakes, and repeated peeling thins some flakes down to a single carbon sheet. That single sheet, one atom thick, is still a crystal — its honeycomb order is visible directly in an electron microscope.
Strong in-plane bonds, weak van der Waals bonds between sheets: a layered crystal peels down to one sheet.
Two-dimensional does not mean flat with no thickness — it means one or a few atoms thick, with the crystal's periodicity living only in the plane. It is distinct from a quantum well: a 2D material is a free-standing atomic sheet bonded to neighbours by van der Waals forces, not a layer buried inside a 3D crystal and held by ordinary bonds.