“Two dimensions are golden,” says of the University of Manchester, UK. Physics in one dimension is too simple to be satisfying, and three dimensions are complicated and messy. Two-dimensional “flatland” is just right, with just enough room for interesting and useful things to arise. “As a physicist, this is the dimension you would like to live in,” says Geim.
He would say that. Geim was one of the team that in 2004 produced the first 2D material, sheets of carbon one atom thick known as graphene. Graphene could indeed be incredibly useful, with electrons shooting across its sheets almost unhindered. If 1D nanotubes are the wires of future computers, graphene could be their circuit boards.
That’s not all. Take high-temperature superconductors. We already know of materials that conduct with absolutely no resistance at temperatures up to around 130 kelvin, just under halfway from absolute zero to room temperature. We’d love to know how they do it, but after 20 years of head-scratching all we know is that the effect seems to arise from the formation of 2D “sٰ” of electrical charges. If we could fully fathom the physics behind that, it could set us on the path to superconductors that work even at room temperature.
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So flatland is practical, but it is also profound. When electrons are confined by powerful magnetic fields to a 2D layer of semiconducting material cooled to less than one-third of a degree above absolute zero, electrons – which were long considered fundamental, indivisible particles – appear to break down into particles each with just a fraction of the electron’s charge.This phenomenon is known as the fractional quantum Hall effect, and the resulting particles are ambiguous characters dubbed anyons.
Anyons not only force us to rethink the nature of the electron, but might also, like zero-dimensional quantum dots, represent a great hope for building an ultrapowerful quantum computer. If we could get such a machine to work on a significant scale, it would perform astonishing feats of information processing, and could also faithfully model the behaviour of quantum systems. In short, flatland may open grand vistas on everything from new drugs to parallel universes.
Read more: Beyond space and time