David J. Thouless (1934-2019) Theoretical Physicist Who Discovered Topological Phases of Matter

OBITUARY COMMENT David J. Thouless (1934-2019) Theoretical physicist who discovered topological phases of matter.

avid Thouless was best known been largely overlooked. Kosterlitz and for his work on what drives the Thouless realized that, at low temperatures, a rearrangement of the constituents topologically ordered phase existed in which Dof systems, such as the atoms in a crystal or interacting pairs of vortices are thermo the spins associated with the electrons in a dynamically stable. At higher temperatures, magnet. These ‘ordering phenomena’ under- these vortices unbind and move away from lie phase transitions, for example when water each other, and are eventually destroyed by becomes ice. the system’s entropy. In the early 1970s, Thouless predicted Independently, Kosterlitz followed up a particular type of ordering, along with this work with a more rigorous theoretical his colleague Michael Kosterlitz. The derivation. More importantly, perhaps, other Kosterlitz–Thouless transition has since research groups were able to demonstrate the been observed in superfluids, superconduc- Kosterlitz–Thouless transition experimen- tors , magnets and other two-dimensional tally. The most famous of these demonstra- quantum systems. It was largely for this con- tions, carried out by David Bishop and John tribution that Thouless and Kosterlitz shared Reppy in the late 1970s, used thin films of a physics Nobel prize in 2016 with another superfluid helium. But the beauty of the vor- theorist, Duncan Haldane. tex-unbinding mechanism is its universality. A deep and original thinker, Thouless The same ideas can be used to describe the made many significant contributions, in behaviour of ultrathin superconductors and areas as wide-ranging as nuclear matter, magnets, for example, as well as the melting

ALEXANDER MAHMOUD/NOBEL MEDIA AB statistical mechanics and condensed-matter of a 2D crystal. physics. A theme of much of his work was In 1980, Thouless joined the University topology, and how it can lead to non-trivial 1959, Thouless returned to the United King- of Washington in Seattle, where he thrived configurations within the constituent parts dom for a postdoctoral fellowship at the until his retirement, along with his wife, who of a system. Over the past decade, the realiza- University of Birmingham, to work on the held a faculty position in pathobiology there. tion that certain topological features, such as collective motion of nuclei. There, he experi In another profound study that was cited by vortices and knots, can arise in the arrange- enced what he later described as the the Nobel committee, he helped to expose ment of electrons in many materials has most interactive time of his career. He the topological origin of the quantum Hall caused a burst of interest in what are known as worked under his mentor, Rudolf Peierls, effect, the stepwise increase in electrical topological states of matter. Researchers aim whose open approach and broad con- conductance seen in ultrathin conducting to use these as building blocks for applications nections (forged during the Manhattan layers at low temperatures. This work estab- in electronics, such as making computing Project) helped to cultivate a world-class lished the conceptual framework that would more energy efficient. This exciting area is Department of Mathematical Physics. eventually allow topological insulators to be the direct offspring of Thouless’s ideas. Birmingham is also where — a decade discovered. Born in Bearsden, UK, Thouless grew up later — Thouless carried out his most Indeed, Thouless’s 1998 book, Topological in Cambridge. Both parents were academics: famous work. Quantum Numbers in Nonrelativistic Physics, his mother lectured in English literature; his Following a few years as a lecturer in which brought together many of the themes father, psychology. Thouless’s aptitude for Cambridge, Thouless was appointed pro- that had interested him throughout his mathematics was recognized early, and his fessor at Birmingham in 1965. During career, is notable for its prescience. More than father instilled in him a deep curiosity and this period, his research interests shifted two decades since its publication, it is more independence of thought that characterized towards statistical mechanics — especially relevant to our modern understanding of his career. the study of phase transitions, a field that was topological phases of matter than ever. After attending Winchester College on undergoing a revolution at the time. By his own account, David Thouless had a scholarship, Thouless studied natural A typical phase transition might involve, an introverted personality, preferring to sciences at the University of Cambridge. say, a magnetic material switching to a collaborate with colleagues rather than lead Here, he met the future Nobel prizewinner non-magnetic state above a certain critical a group. Leaps between stages of his power Hans Bethe, then on sabbatical at the temperature. However, a class of 2D systems ful arguments left many lost until hours Cavendish Laboratory. Bethe invited him (known as continuous spin systems) pre- later. But those who were fortunate enough to do a PhD at Cornell University in Ithaca, sented a conundrum. A rigorous theorem to work with him directly remember him New York. So, in 1956, Thouless set sail for ruled out the stability of an ordered, mag- warmly, both for his gentlemanly demeanour the United States. His experience at Cornell netic phase at low temperature. Yet various and for his brilliant — if economically was a happy one. He worked on the applica- investigations — theoretical, numerical and expressed — scientific insights. ■ tion of perturbation methods to the theory experimental — suggested the presence of a of nuclear matter, and met his future wife, phase transition. Andrea Taroni is the chief editor of Nature Margaret Scrase. How could this discrepancy be resolved? Physics. Next came a stint at the Lawrence Radia The answer lay in the existence of vortices, e-mail: [email protected]; tion Laboratory in Berkeley, California. In topological excitations that had hitherto Twitter: @TaroniAndrea