David J. Thouless
University of Washington, Seattle, WA, USA

and the other half to

F. Duncan M. Haldane
Princeton University, NJ, USA

and

J. Michael Kosterlitz
Brown University, Providence, RI, USA

”for theoretical discoveries of topological phase transitions and topological phases of matter”

They revealed the secrets of exotic matter

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 three Laureates’ use of topological concepts in physics was decisive for their discoveries. Topology is a branch of mathematics that describes properties that only change step-wise. Using topology as a tool, they were able to astound the experts. In the early 1970s, Michael Kosterlitz and David Thouless overturned the then current theory that superconductivity or suprafluidity could not occur in thin layers. They demonstrated that superconductivity could occur at low temperatures and also explained the mechanism, phase transition, that makes superconductivity disappear at higher temperatures.

In the 1980s, Thouless was able to explain a previous experiment with very thin electrically conducting layers in which conductance was precisely measured as integer steps. He showed that these integers were topological in their nature. At around the same time, Duncan Haldane discovered how topological concepts can be used to understand the properties of chains of small magnets found in some materials.

We now know of many topological phases, not only in thin layers and threads, but also in ordinary three-dimensional materials. Over the last decade, this area has boosted frontline research in condensed matter physics, not least because of the hope that topological materials could be used in new generations of electronics and superconductors, or in future quantum computers. Current research is revealing the secrets of matter in the exotic worlds discovered by this year’s Nobel Laureates.

And that's a wrap

There we have it. The 2016 Nobel prize in physics has gone to David Thouless, Duncan Haldane and Michael Kosterlitz for their work on exotic states of matter. The work helps explain why some materials have unexpected electrical properties, such as superconductivity, and in future the work could pave the way for quantum computers.

What's the deal with doughnuts and coffee cups?

For an electrical conductor, for instance copper, scientists can normally define a fixed relationship between how much electrical potential you put across a wire and how much current flows. However, when a material undergoes an electrical phase transition, this relationship goes out the window and the material abruptly takes on completely new electrical properties.

Mathematically, these transitions can be thought of as leaping from one topological form to another. A topological surface is partly defined by how many holes there are. So, in topological terms, a doughnut to a coffee cup (both have one hole) are the same. But a ball is different. These shapes just relate the maths used to describe the properties of a material - we’d like to stress that no physical objects are being magically transformed into doughnuts.

What are phase transitions?

Phase transitions refer to abrupt changes in the properties of a material - for instance the progression from ice to water to steam as the temperature is ramped up from freezing. However, as well as the traditional states of solid, liquid, gas, Thouless, Haldane and Kosterlitz (and others) showed that materials also make sudden transitions in their electrical properties. This might manifest itself as a sudden drop in the electrical resistance of a material as it is cooled down. So-called topological phase transitions were initially investigated in materials with thin layers, or ones that formed thin threads, but now scientists have shown that “exotic” electrical properties can be found in a wide range of materials.

Thouless, Haldane and Kosterlitz have investigated these phase transitions and also come up with important pieces of the theory that explains why these sudden changes happen.

Here’s some reaction from Steve Bramwell, a physics professor at the London Centre for Nanotechnology, who is working in the field:

I think the Nobel prize to Kosterlitz, Thouless and Haldane is richly deserved!

The behaviour of the materials around us is extremely complex - the job of physics is to identify simple principles by which we can understand the material world and predict new phenomena. This is a really difficult challenge because the average substance may contain a trillion trillion atoms, all interacting with each other.

The ingenuity of Kosterlitz, Thouless and Haldane has been to show how a large class of real materials - particularly films and chains of atoms - can be understood in terms of the simple mathematical principles of topology - that is how the atoms are connected (a doughnut and a teacup have the same topology as they each have a hole in them).

The breakthroughs of these three scientists allowed massive progress to be made in understanding and calculating the properties of many material systems.

I’m sure this Nobel prize will be cheered in many quarters!”