Topological Protection and Non-Equilibrium States in Strongly Correlated Electron Systems

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A paper mbius strip is like a cylinder in which the paper twists as it goes round. It looks looks quite like the simple cylinder, but it cannot be transformed into one without some drastic action such as cutting it with a pair of scissors. The mathematics describing this fact is known as topology. It allows the classification of shapes and objects into sets whose members are fundamentally similar to each other, and fundamentally different from objects in other sets. This seems abstract, and it is. However, abstract concepts can sometimes point the way to futuristic applications of sciences. One of the ambitious dreams of modern physics and electrical engineering is to build a quantum computer, a machine that would function completely differently to today's computers, and be a step-change in technology. In order to do that, one has to harness a property of quantum mechanics called 'coherence', which allows its laws to be realised. In the everyday world, fully coherent systems are extremely rare, because when they couple with everything around them, that environment acts like a source of strong random noise that scrambles the system up. This 'decoherence' is one of the core problems of the field. Ground-breaking theoretical research over the last decade has shown that there might be special classes of quantum system which are topologically distinct from the vast majority of other systems. This means that they will not couple to the environmental noise that is such a problem, and offer a route to overcoming decoherence. The second key issue for an electronics revolution is understanding what happens when you severely disturb even a normal quantum mechanical system. This is called driving it from equilibrium, and is going to be more and more important as we try to make electronics run faster and over smaller distances. We understand equilibrium quantum physics very well, but as soon as we go far from equilibrium we enter unexplored territory.In this Programme, we will address both these issues. Building on a breakthrough which has shown that topology is much more important in modern materials than we had ever suspected, we will perform a series of interlinked projects aimed at establishing which materials are most likely to offer topological protection from decoherence. Although ambitious, this is not an empty dream. Microsoft, who formally support our work, have created an entire research centre in the USA to work towards it. Their efforts are mainly theoretical, while ours will be mainly concerned with concrete experiments both on naturally occurring materials and on specially engineered hybrids. The second thrust of our Programme, non-equilibrium quantum mechanics, will be mostly theoretical work to begin with. Its primary focus will be gaining insights that will be of relevance to futuristic electronics in general, but we believe there is particular value in coupling that work with the investigation of topological effects. Nothing is proven yet, but there are good grounds to think that non-equilibrium systems may themselves ultimately prove to be the best platform for stablising the topological excitations that so many people are seeking.Our work is highly adventurous, and will push back the frontiers of current knowledge. Doing it as a co-ordinated Programme will bring exactly the cross-fertilisation of ideas and techniques, and of experiment and theory, that maximises the chances of success. The scale of a Programme also enables engaging with top international collaborators. In addition to working with Microsoft's research centre, we will exchange ideas and personnel with groups from Harvard, Berkeley, Cornell and Princeton in the USA, Grenoble in France and Tokyo and Kyoto in Japan. Major challenges require this level of global collaboration, which will expose the young people who we will train to the very best minds.