Lee Billings in Scientific American:
The Nobel Prize in Physics 2016 was split, with one half going to David J. Thouless at the University of Washington, and the other half going to F. Duncan M. Haldane at Princeton University and J. Michael Kosterlitz at Brown University. The Prize was awarded for the theorists’ research in condensed matter physics, particularly their work on topological phase transitions and topological phases of matter, phenomena underlying exotic states of matter such as superconductors, superfluids and thin magnetic films. Their work has given new insights into the behavior of matter at low temperatures, and has laid the foundations for the creation of new materials called topological insulators, which could allow the construction of more sophisticated quantum computers.
Topology is a branch of mathematics that studies properties that only change incrementally, in integer steps, rather than continuously. Thors Hans Hansson, a physicist at Stockholm University who served on this year’s Nobel Committee, explained the core concept of topology during the awards announcement by pulling a cinnamon bun, a bagel, and a Swedish pretzel from a bag. “I brought my lunch,” he joked, then explained that, to a topologist, the only difference between the three foods was the number of holes in them, rather than their taste. A cinnamon bun has no holes, while a bagel has one and a pretzel has two. To a topologist, then, the bun would fall in the same category as a saucer, while the bagel would be paired with a cup, and a pretzel with a pair of spectacles. Thouless, Kosterlitz and Haldane’s prize-winning insights revolve around the idea that these same sorts of “topological invariants” could also explain phase changes in matter, albeit not familiar ones such as a liquid freezing to a solid or sublimating to gas. Instead, the phase changes the theorists studied took place chiefly in thin two-dimensional films cooled to cryogenic temperatures.