Loosely, it refers to the degrees of freedom an electron has in the material. For example, if you consider the 'density of states' – a quantity which can be tho

Loosely, it refers to the degrees of freedom an electron has in the material. For example, if you consider the 'density of states' – a quantity which can be thought of as the number of electrons at a given energy level – it has a different characteristic shape depending on whether the material is '1D', '2D', '3D' or even '0D': http://britneyspears.ac/physics/dos/images/Image441.gif http://britneyspears.ac/physics/dos/images/Image441.gif [As an aside, britneyspears.ac is a surprisingly good resource for a lot of basic solid state physics. You can find a full derivation of the above graph on there.] Edit: To illustrate, this next graph is the density of states for three different Carbon-based materials: graphite which is '3D', graphene which is '2D' and a nanotube which is '1D'. http://me3007.wdfiles.com/local--resized-images/thermal-and-electronic-properties-of-carbon-nanotubes/QuantDOS.jpg/medium.jpg http://me3007.wdfiles.com/local--resized-images/thermal-and-... [Source: Hone, J., Quantized Phonon Spectrum of Single-Wall Carbon Nanotubes, Science, 289, 1730, 2000 via http://me3007.wikidot.com/thermal-and-electronic-properties-of-carbon-nanotubes http://me3007.wikidot.com/thermal-and-electronic-properties-...] You can see how these curves are similar to the theoretically-derived curves in the previous graph.