A strip of a only a few nanometres wide – a ribbon cut, or grown, from a sheet. At that width the edges matter as much as the middle. The electrons are squeezed sideways, so graphene, which normally has no , gains one that grows as the ribbon narrows, and the shape of the edge, zigzag or armchair, changes how the ribbon behaves. Ribbons assembled from molecules have exactly defined widths and edges; ribbons of MoS2 and other are studied as the narrowest possible channels.
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Cutting graphene into nanoribbons a few nanometres wide, or putting an electric field across a bilayer, does open a gap, but none of these yet gives a switch that competes with silicon.
A graphene ribbon has two kinds of edge, and a band gap that grows as it narrows. The graph is schematic: real gaps also depend on the edge and on the exact number of rows of atoms.
Width makes a gap
In a sheet of graphene the electrons can move freely in both directions, and the conduction and valence bands touch. Cut the sheet into a strip and the sideways motion is confined: only certain standing waves fit across the width, as only certain notes fit on a guitar string, and the bands separate. The narrower the ribbon, the larger the gap – roughly in inverse proportion to the width.
The ribbons have to be very narrow for this to matter at room temperature. A ribbon 10 nm wide has a gap of the order of 0.1 eV, while the seven-atom-wide armchair ribbon, under a nanometre across, has a gap of over 2 eV when measured on gold – a semiconductor made of graphene.
Edges decide
A ribbon’s edges run either along the zigzag direction of the or along the armchair direction, at 30 degrees to it. In armchair ribbons the gap depends not only on the width but on the exact number of rows of carbon atoms across, in a pattern that repeats every three rows: a ribbon one row wider can have a much smaller gap. Zigzag edges carry states of their own, flat in energy and confined to the edge, which calculations predict to become magnetic, with opposite on the two edges.
Real edges also carry chemistry: hydrogen, oxygen or other groups end the broken bonds, and roughness of even a few atoms scatters electrons and traps them. That is why ribbons cut by lithography and behave mostly as chains of small islands, and why atomically precise edges matter.
Making them
Ribbons can be cut from a sheet by electron-beam lithography and etching, made by unzipping carbon nanotubes lengthwise, or grown. The most precise route builds them from molecules on a gold surface: halogenated precursor molecules are evaporated onto Au(111), linked into polymer chains on gentle heating, and then flattened into graphene ribbons at a higher temperature as hydrogen leaves. Every ribbon has the same width and edge, set by the molecule, and designed precursors give junctions, kinks and end states.
The catch is the gold: the ribbons must be onto for devices, and they are short, often tens of nanometres. Ribbons of MoS2, WS2 and other semiconductors are grown along the steps of a substrate or from the edges of existing layers, aiming at channels narrower than lithography can define.
For specialists
A quasi-one-dimensional strip of a layered crystal, typically 1–50 nm wide, whose is set by lateral confinement and by edge termination. Armchair graphene ribbons fall into three families by the number N of carbon dimer lines across them (N = 3p, 3p + 1, 3p + 2), all gapped, with gaps falling roughly inversely with width; zigzag ribbons carry that are predicted to order magnetically.
Lithographically cut ribbons have rough edges that localise carriers, so their transport gaps reflect as much as confinement. Bottom-up synthesis on Au(111), by surface polymerisation of halogenated molecular precursors and cyclodehydrogenation, gives atomically precise widths and edges and allows designed junctions, including ones with topological end and junction states. nanoribbons grown along substrate steps or by edge-directed growth are studied for channel-width scaling beyond transistors.
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