Graphene is a single layer of carbon atoms, arranged hexagonally, in a chicken-wire structure. Layers and layers of it make up the much more familiar graphite — pencil lead.
So why is a pencil not worth thousands of pounds? Why is graphene so startlingly different from graphite? This is really the same as asking: what does it mean to create a truly two-dimensional thing, to have a sheet of atoms you can hold in your hand?
For a start, it means electrons behave rather differently. In graphite, the electrons associated with the carbon atoms interact with each other between the layers to stick the sheets together in a mass. Once this electron coupling is gone, things start to get interesting.
Normally, electrons moving in a solid have a small effective mass associated with them, resulting from their interactions with the stuff all around them. Without these interactions, as in a sheet of graphene, electrons behave as though they are massless particles, moving freely through empty space, at close to the speed of light.
It means the electrons' behaviour is described by the Dirac equation (conceived by physicist Paul Dirac in 1928 to account for relativistic motion of particles like electrons). As a result, people have started referring to them as Dirac fermions.
Switching to two dimensions sets the electrons free and allows carbon to behave in totally new ways.
This is what allows graphene's astonishing conductivity, which is some 35 percent better than copper. It is also why electron transport in graphene is 1,000 times better than in silicon. It also explains why graphene maintains a minimum conductance, even when concentrations of electrons in the material tends to zero.
Switching to two dimensions sets the electrons free and allows carbon to behave in totally new ways. But it turns out — to everyone's surprise — that you don't only see this weird behaviour in single layers of graphene.
Electrons behaving like Dirac fermions have been spotted in multi-layered graphene as well. Scientists have found that varying the alignment changes the freedom of the electrons: some angles increase electron coupling between the layers, making the electrons behave more normally. Others hardly interfere with the unusual nature of graphene, allowing the layers to be considered as individual two-dimensional systems.
And these double-layer systems are proving particularly interesting, as Dr Leonid Ponomarenko of Manchester University explained. "My research at the moment is focused on double-layer graphene structures," he told ZDNet UK. "In such devices two graphene sheets are separated by a very thin dielectric. The separation is so small that interactions between electrons in two layers became significant and we can observe a whole range of new interesting phenomena."
The layers of graphene and dielectric work as a tunnelling transistor, he explained, when they are placed on an oxidised silicon wafer. The wafer acts as an electrostatic gate, so the whole set-up offers an alternative approach for making graphene-based field effect devices.
Scientists including Nobel laureates Klaus von Klitzing (discoverer of the integer quantum Hall Effect) and Albert Fert (discoverer of giant magnetoresistance) are busily researching other candidates for two-dimensional life, such as boron nitride and bismuth, and the weird and wonderful properties they might reveal.
The potential is astonishing — especially when you consider how graphite's properties are transformed, just by freeing a layer from its lattice. Many other substances can be reduced to a single or bi-layer state, and could be used alone, or in combination with graphene to create entirely new materials. Graphene might have been the first, but it is unlikely to be the last.
In the last part in our series, we look at the future of graphene.
Read more of ZDNet UK's special coverage of Graphene: Future IT.