Over the past week, this year’s Nobel laureates have been announced in the fields of physics, chemistry, psychology and medicine, economics, literature and peace.
The Nobel prize for physics this year was awarded to three British scientists (David J Thouless, F Duncan M Haldane and J Michael Kosterlitz) for their theoretical discoveries relating to ‘topological phase transitions and topological phases of matter’. In the early 1970s, Kosterlitz and Thouless disproved the theory that superconductivity could not occur in extremely thin layers. They explain how superconductivity can occur at low temperatures and that the mechanism of phase transition prevents it from occurring at higher temperatures. Around a decade later, Haldane also studied matter that forms threads so thin they can be considered one-dimensional.
All of these studies centred around the use of the mathematical principles of topology, and whilst it would be difficult for me to explain the exact findings of their work, topology is fairly easy concept. It concerns transforming one shape into another by means of stretching or bending but not cutting or gluing. Any two shapes that can be transformed into each other by this method are considered homeomorphic or topological twins.
For example, if you print out every letter of the alphabet onto a rubber sheet, which letters can be stretched into the shape of another letter? Topologists like to consider the most fundamental properties of shapes in order to investigate their topological nature. The letter A is essentially a loop with two legs, as is the letter R. Therefore, it can be said that A and R are homeomorphic. However, the letters H and A are not homeomorphic even though they seem very similar in shape because an H contains no loops. To turn an H into an A, you would have to either glue part of the H together or cut apart the A. This same theory works for three dimensional objects as well, for example, a coffee cup and a doughnut are homeomorphic because both of them only have one loop: the handle of the coffee cup and the centre of doughnut, it’s created by the centre.
But why is discovering the topological nature of exotic states of matter important for science? For one thing, their research could be used in the next generation of electronics and superconductors, or quantum computers, as the Nobel Committee member Thors Hans said: ‘People are working very hard in the labs to get new materials which have interesting properties of conducting electricity’.The findings of this year’s physics Nobel Laureates could be pivotal in providing new materials for the use of superconductivity in order to carry information or code for quantum computers more effectively, therefore making this an instrumental and fascinating revelation in science.