David Thouless, Duncan Haldane and Michael Kosterlitz, who all now work at U.S. universities, share the prize for their discoveries on abrupt changes in the properties, or phases, of ultra-thin materials.
Their research centers on topology, a branch of mathematics involving step-wise changes like making a series of holes in an object. The difficult-to-grasp concept was illustrated by Nobel Committee member Thors Hans Hansson at a news conference using a cinnamon bun, a bagel and a pretzel.
Phases are obvious when matter goes from solid to liquid to gas, but materials can also undergo topological step changes that affect their electrical properties. One example is a superconductor, which at low temperatures conducts electricity without resistance.