This year, the Nobel Prize in Physics has been awarded to David J. Thouless, F. Duncan M. Haldane and J. Michael Kosterlitz for “theoretical discoveries of topological phase transitions and topological phases of matter.” One half of the prize goes to Prof. Thouless and the rest to Prof. Haldane and Prof. Kosterlitz.
While Prof. Kosterlitz and Prof. Thouless studied phase transitions in two-dimensional (flatland-like) systems, Mr. Haldane studied thread-like one-dimensional matter models. From explaining Quantum Hall Effect to new topological materials, their work has thrown open huge areas in condensed matter physics.
Prof. Haldane, when contacted by the Nobel committee after the prizes were announced, said that when he worked on the problem in the late 1980s, it “seemed abstract and was of mathematical and scientific interest. I did not think it would ever find practical applications...”
Speaking of how he came up with the idea, he said of big discoveries, “You never set out to discover them. You stumble upon it and then realise you have discovered something. It takes a while, and when you do, you wonder why someone else did not discover it…”
Topology, the study of geometric properties of the medium in question, is the unifying theme of the work done by the three scientists. This sounds, and is, very mathematical; the scientists’ special achievement is in taking deep mathematical concepts and using them to prove some very fundamental aspects of physics.
Meeting point of topology and phase transitions Their work rests in a meeting point of topology and phase transitions. One can observe different phases of materials; for example water, which exists as solid, liquid or gas. The material can undergo transitions from one phase to another, just as water evaporates into vapour. When you cool some substances to very low temperatures, you can encounter exotic phases. Such phases were studied by these scientists, who characterised the phases using a sophisticated geometrical concept — topology. To see what topology entails, compare a ball and a cup. These are different topologically because all closed loops placed on the surface of the ball can be shrunk to a point, while the same cannot be said of the cup, which has a “handle”.
Senior condensed matter physicist G. Baskaran of the Institute of Mathematical Sciences, Chennai says, “Kosterlitz and Thouless’ work on planar X-Y model came into condensed matter physics in a big way. They described non-trivial effects, which could not be reproduced simply. We knew it was a paper that was going to make a change in physics.” Prof. Baskaran describes how the influence of their work is reflected even in high-energy physics and string theory.
Prof. Haldane, according to Prof. Baskaran, “worked-in topology in profound ways”. Prof. Baskaran refers to developing an understanding of Quantum Hall Effect. The influence of Prof. Haldane’s work stretches on: From forming the basis of topological field theories to the Haldane-Sastry model, to topological insulators and conceptualising the “Haldane gap,” a critical parameter in the study of chains of antiferromagnetic atoms.
Indians have developed this field further and made important contributions. For example, J.K. Jain’s work on composite fermions is famous. The work on topological insulators by C.L. Kane et al is another significant work which take up where they leave off. As Prof. Baskaran puts it, “This prize clears the way for other Nobel prizes.”
