“This year’s Nobel Prize in Physics has been awarded to David J. Thouless of the University of Washington, Seattle, F. Duncan M. Haldane of Princeton University, and J. Michael Kosterlitz of Brown University for “theoretical discoveries of topological phase transitions and topological phases of matter.” The prize is divided with one half going to Thouless and the other half split between Haldane and Kosterlitz.

According to the citation from the Royal Swedish Academy of Sciences, this year’s laureates opened the door on an unknown world where matter can assume strange states. They have used advanced mathematical methods to study unusual phases, or states, of matter, such as superconductors, superfluids, or thin magnetic films. Thanks to their pioneering work, the hunt is now on for new and exotic phases of matter. Many people are hopeful of future applications in both materials science and electronics.

The laureates are theorists who, in the 1970s and 1980s, laid the foundations of the study of so-called topological states of matter, which in recent years have been perhaps the hottest topic in condensed matter physics. The theoretical concept has some simple, straightforward physical manifestations. For example, it can explain how a material such as an alloy of bismuth and antimony can be an electrical insulator on its inside but an electrical conductor on its surface. However, the theory itself is subtle and abstract and plays on the differences in shapes in abstract spaces.

The key is mapping, say, the interactions of electrons in a solid, in a particular way in an abstract parameter space. That mapping can produce weird shapes, rather like abstract sculptures, that have different topologies or numbers of holes—just as a donut has one hole and a six-pack holder has six. Those numbers act like unchangeable “charges” and can lead to striking effects. For example, an insulating material can become conductive at its surface because, when mapped in this way, the interactions among the electrons have different topologies in the material’s bulk and on its surface. So even though both interior and surface ought, at first blush, to be insulating, near the surface things have to go a little haywire as the topological charge changes. That loosens things up so electrons can flow and the material conducts.

Thouless, Haldane, and Kosterlitz laid the conceptual foundations for such a topological approach to condensed matter physics by studying other systems in reduced dimensionality—such as 2D films of liquid helium or electrons confined to 2D planes in layers of ultrapure semiconductors. That approach is now a hot topic as experimenters look for new solid materials that demonstrate such effects.”

Source: Trio snare physics Nobel for describing exotic states of matter | Science | AAAS