For their theoretical work explaining strange states of matter, including superconductors, superfluids and thin magnetic films, the 2016 Nobel Prize in Physics has been awarded to three British scientists working in the U.S.

The award was split between University of Washington’s David J Thouless, Princeton’s Duncan M Haldane, and Brown University’s J Michael Kosterlitz. They’re going to share a US$ 928,000 sum. Their work has helped shape an enormous amount of research over the past three decades and this well-deserved prize reflects the continuing importance of new discoveries that have and will continue to emerge.

You are probably familiar with “normal” state of matter: solids, liquids, and gases. The transition between these states is characterized by the so – called “symmetry break.”

For instance, atoms are uniformly arranged in space in a liquid and it looks identical regardless of how you rotate it. However, the atoms are locked into a crystal lattice when a liquid becomes a solid. This new state of matter is less symmetrical in the sense that when it is rotated at certain angles it only looks the same.

Thouless, Haldane and Kosterlitz, however, found the matter to be much more interesting than this. Their work showed how new phases of matter can occur when no symmetry is broken–and to explain this they used a mathematical idea. What distinguished these phases of matter–showing strange behaviors such as unusual electrical conductivity patterns–were “topological properties.”

Topology is the mathematical study of how surfaces can be deformed continuously and smoothly. A famous example is the surface of an orange, a croissant, a coffee cup and a doughnut. To a mathematician, all these objects are imagined to be made of a malleable material that we are allowed to deform continuously without cutting or tearing.

An orange and croissant are identical in this way, as we could shape both into a sphere. Similarly, a mathematician also has the coffee cup and doughnut because they both have one hole – the cup has a hole in its handle and the doughnut in its center.

So the orange and croissant are in a distinct class in this abstract sense, while the coffee cup and doughnut are in another class. The difference between them is whether or not their surface has a hole in it. This is the object’s topological property that is robust to any moulding we could do. Thouless, Kosterlitz and Haldane’s work has taken important steps to understand how the notion of topology plays a role in the phases of matter.

This connection was exposed by considering the energies that can be occupied by electrons in materials – which can be plotted as a surface (shown as a function of their momentum).

In the 1980s, scientists discovered that when subjected to a strong magnetic field, electrons in certain two-dimensional thin films move in a strange way. These electrons arrange in perfectly conducting channels, situated at the edge of the material, based on a mechanical quantity known as spin.

Moreover, as the magnetic field increases, this conductivity increases in discrete steps–an effect called the effect of the quantum hall. Thouless and coworkers found that, in topological terms, the “energy surface” for these materials could be described as a doughnut, and the energy channels seen were the number of holes in that surface.

Along with further work on other systems by Kosterlitz and Haldane, such as vortices superconductors and hidden ordering in magnetic materials, their work showed that the topology idea could be used to predict solid behavior.

Great promise

The work of Thouless, Kosterlitz and Haldane has laid the groundwork for new emerging fields. In a field of solid state physics called topological insulator materials, they were particularly crucial. These are new three-dimensional materials carrying electricity on the surface, but not on the inside.

Topology can also describe their energy surface. These materials have many “spintronic applications,” and hard drive heads are currently being used in industry based on this technology.

As a result of some energy transfer, technological applications of materials often rely on how they act when they are “excited.” If we shake it at one end, we can imagine an excitement as being a bit like a pulse traveling down a string.

One device being studied is made of topological insulator layered above a superconductor (a material with zero electrical resistance at low temperatures). If we poke this system in the right way, the interface between the materials will be excited. These excitations carry a topological property, like a hole in a doughnut, robust in the face of noise and imperfections.  that might scatter the excitation (which could be some sort of signal).

For quantum computing, this effect is potentially very useful. In a normal computer, the “bits” of data are 1 or 0. A quantum computer, however, uses quantum bits, which may be in state overlays (according to quantum mechanics) – making calculations super fast.

Currently scaling up quantity computing to commercially applicable sizes is hampered by external environment noise, such as shaking something. However, the information encoded in them could be protected and preserved by exploiting excitations from topological materials.

This is an exciting research avenue that could help revolutionize the technologies of information processing.

Stephen Clark, Lecturer in Physics, University of Bath

This article was originally published on The Conversation. Read the original article.

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