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

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.

The world-wide drive to maintain the pace of the electronics revolution demands ever smaller basic elements, working ever faster. This inevitably means that quantum mechanics will play a role of increasing importance in future technology. We must either work around quantum physics, attempting to suppress the effects of its intrinsic uncertainties and fluctuations, or work with it. In this Programme we aim to work with it, investigating how to realise coherent quantum control using futuristic 'topological' excitations. In parallel and in combination with this, we will tackle the problem of non-equilibrium quantum physics, whose understanding will be of ever-increasing importance as we ask more and more of electronic materials. Our work lies somewhere between fundamental and applied research - it is an example of focusing abstract mathematics and physics with a long-term technological goal. Deep and basic questions still need to be addressed, and the field is still a long way from the market-place, but it attracts significant attention from an industry that knows that a paradigm shift will be needed if progress is to be maintained. Indeed, Microsoft formally support our Programme, and will work with us throughout its duration. To ensure that the benefits of our long-term research are available more broadly to industry, we will establish an Industrial Associate scheme to ensure good communications with other potential users such as Toshiba and Hitachi, who, like Microsoft, are significant inward investors in the UK. This will build on a model that we have piloted successfully in setting up the Scottish Doctoral Training Centre in Condensed Matter Physics. Many of the elite students in that Centre will also work on research projects offered by the Programme. They, as well as the post-doctoral research associates who we employ, will be one of our outputs, namely a supply of people with a breadth of training that is of direct relevance to the development of future technologies. Other ways in which we can benefit the economy are perhaps best classed as 'spin-off' and 'spin-out'. The former will be achieved because the advanced materials in which we will investigate topological effects also have likely uses in other ways. One family, for example, has potential to be used in thermoelectric refrigeration. In terms of direct spin-out, the most likely output is the commercialisation of some of the unique instruments that we build in order to make the highly sensitive measurements that are necessary for our research. We will also make use of the opportunities afforded by work like this for advocacy and outreach. The story of the field is a compelling one: mathematics developed in the era of Kelvin for a 'failed' atomic theory found relevance in the twenty-first century in a futuristic model for quantum computation that is now being pursued by scientists across three continents and four core fields: mathematics, physics, computer science and electrical engineering. Base material of that quality provides an excellent platform from which to inspire a range of audiences from the young to the old. We will establish, and resource, a formal outreach and advocacy programme to ensure that society profits fully from it. A final form of impact concerns contributions to the international reputation of UK science. Our team are all international leaders in their fields, and direct collaboration between our Programme and institutions such as Berkeley, Cornell, Princeton, Harvard, Tokyo and Kyoto ensures that as well as our young team members receiving training to the highest international standards, ours will be work of international prominence. This will be of particular importance as the UK faces a difficult period in which international perception of its achievements assumes greater than normal significance.