The 2016 Nobel prize for physics goes to three unexpected recipients

YOU cannot have half a hole. That is the essence of topology, a branch of geometry which deals in “invariants”, such as holes, that can exist in geometric shapes only in discrete, integer numbers. This year’s Nobel prize for physics has gone to three researchers who have applied topology to materials science, and have come up with theoretical explanations about the behaviour of unusual states of matter as a result.

The winners are David Thouless of the University of Washington, in Seattle, Duncan Haldane of Princeton University, in New Jersey, and Michael Kosterlitz of Brown University, in Providence, Rhode Island. All three are products of the 20th-century “brain drain” that saw British-born researchers head west to the larger salaries and better laboratories of America.

Dr Thouless, who takes home half of the SKr8m ($930,000) prize, collaborated with Dr Kosterlitz, who shares the other half with Dr Haldane, in the 1970s, when both were still in Britain. The fruit of their collaboration was to overthrow the idea that superconductivity (a phenomenon in which the resistance of an electrical conductor vanishes, usually when it has been cooled to a temperature near absolute zero) could not occur in thin layers of material. It could, according to their calculations, because of the effects of paired vortices within such a layer. Vortices, a type of hole, are topological invariants. It is the liberation of these vortices to move around as a material warms up which destroys superconductivity. Such liberation is, in effect, a phase change from one state of matter to another, just as the liberation by heat of atoms from a crystal lattice causes a phase change from solid to liquid.

Dr Thouless then went on, after he had moved to America in the early 1980s, to show that stepwise transitions to and from full superconductivity in the presence of a magnetic field (a phenomenon known as the quantum Hall effect) are also a type of topological invariant. And in the late 1980s, after his own transatlantic migration, Dr Haldane showed that magnetic fields need not be involved in the process at all.

It is, then, esoteric stuff, as the panel announcing the prize admitted. The panelists emphasised the beauty of the underlying mathematics and de-emphasised the practical applications—of which, in truth, there are few. Moreover, the choice of this year to highlight this particular work was a surprise to many observers, who had thought the discovery in 2015 of gravitational waves, by an experiment called LIGO, might win. That would have been in the spirit of Alfred Nobel’s will, which refers to his posthumous awards as being for work from the previous year. For whatever reason, though, the great and good of Sweden’s Royal Academy of Science, who choose the winners of the physics prize, decided to continue the tradition of ignoring this part of the prizes’ founding document. 

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