Lehtikuva/Roni Rekomaa/REUTERS, Kiloran Howard/Trinity Hall/University of Cambridge, Dominic Reuter/REUTERS
David Thouless, Duncan Haldane and Michael Kosterlitz have won the 2016 Nobel Prize in Physics for their theoretical explanations of strange states of matter in two-dimensional materials, known as topological phases.
The trio’s work in the 1970s and 1980s laid the foundations for predicting and explaining bizarre behaviours that experimentalists discovered at the surfaces of materials, and inside extremely thin layers. These include superconductivity — the ability to conduct electricity without resistance — and magnetism in very thin materials.
At the time, these mathematical theories were quite abstract, said Haldane in an interview with the Nobel Commitee just after winning the prize. He said that he was “very surprised and very gratified” to receive the award.
But physicists are now exploring similar states of matter for potential use in a new generation of electronics, and in quantum computers. And the theories pioneered by the Nobel winners have been extended to develop exciting materials such as topological insulators — which don't conduct electricity in their bulk but do on their surface.
Physics through topology
The three winners all explained the behaviour of exotic matter through the mathematical concept of topology, which describes properties that remain unchanged if an object is deformed but not torn.
"In different ways, they showed how the concept of topology could give rise to new forms of matter that hadn’t previously been understood,” says Nigel Cooper, a theoretical physicist at the University of Cambridge, UK.
Just as a knot tied in an unbroken circle of string cannot be removed without cutting the string, topological properties tend to be robust. For example, vortices in a fluid are easy to move around but harder to destroy. “Because of topology, they’re protected. They cannot be simply removed,” explains Immanuel Bloch, an experimental physicist who has studied topological phenomena at the Ludwig Maximilian University in Munich, Germany.
Thouless and Kosterlitz, working at the University of Birmingham, UK, used topology to explain certain kinds of phase transition. Atoms in different phases of matter — such as a solid, liquid or gas — have characteristic kinds of order. In the 1970s, researchers believed that order in a 2D material was impossible, because thermal fluctuations would destroy any ordering, even at temperatures close to absolute zero.
But Thouless and Kosterlitz showed that topological phase transitions — in which a material switches between states with different topologies — were possible in thin layers of materials. Using this model they demonstrated that, in theory, superconductivity could occur at low temperatures, but that it would disappear at higher temperatures. They also explained the mechanism that would make the effect vanish.
Their theory, known as the Kosterlitz–Thouless (KT) transition, turned out to apply to many different kinds of 2D material, and became a useful tool throughout physics. (Vadim Berezinskii, a Ukrainian physicist who presented similar ideas and whose name is usually associated with the transition along with Kosterlitz and Thouless, might have been in line for the prize, but he died in 1980.)
In 1982, Thouless also explained a phenomenon known as the quantum Hall effect — it had been discovered in 1980 by German physicist Klaus von Klitzing, who would go on to win the 1985 physics Nobel prize for his finding. In this odd effect, when electrons are confined to thin films, chilled to near absolute zero and subjected to a strong magnetic field, they flow in an unusually orderly way with conductivity that increases in steps with an increasing magnetic field.
Thouless showed that the quantum Hall effect was, again, a topological phenomenon. Changes to the system’s properties could not occur smoothly — which would be mathematically similar to ‘deforming’ the topological system — but had to occur in sudden steps.
The quantum Hall effect was a huge surprise, says Roderich Moessner, a theoretical condensed-matter physicist at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany. "Thouless realized that topology was a central ingredient."
Haldane, meanwhile, was busy applying the concept of topology to chains of magnetic atoms. These atoms have a quantum property known as spin, and in 1982, he predicted that certain chains of the atoms could show topological properties that result in half spins at either end. Because this quantum property depends on the collective action of the whole chain, rather than on any individual particle, similar phenomena are now being explored as robust ways to encode information in a quantum computer.
The British-born theorists now all work in the United States: Thouless at the University of Washington, Seattle; Kosterlitz at Brown University in Providence, Rhode Island; and Haldane at Princeton University in New Jersey. They will split the prize money of 8 million Swedish kronor (US$940,000), half going to Thouless and the other half split between Kosterlitz and Haldane.
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