Superconductivity is a decrease of the electrical resistivity to zero, in certain materials and at sufficiently low temperature. It is widely employed for high-power applications and extreme magnetic fields - for example, in MRI/NMR machines in healthcare, in high-output wind turbines, and in magnetically-levitated high-speed trains. The global superconductor market is currently estimated at over £5.5B, and is expected to double by the next decade. Superconductivity is a remarkable manifestation of quantum mechanics on large length scales, and underpins some of the most exciting technological possibilities. One of them is the emerging field of quantum computation, in which the most promising prototypes are based on solid-state superconducting chips.

However, superconductivity is a delicate state: it requires low temperatures, and limits on the ambient magnetic field. Many known materials with robust superconductivity have difficult mechanical properties. There is therefore enormous scope for optimisation of superconducting materials, with huge technological and economic benefits. The most promising candidates for a more practical high-temperature superconductor are the so-called "unconventional" superconductors, in which strong and complex correlations between many electrons induce particularly robust superconductivity. They may ultimately provide a route to room-temperature superconductivity. However, our ability to control high-temperature superconductivity has remained severely limited. One of the main challenges is complexity: the strong interactions among electrons often cause them to order in other ways, such as into ribbons of charge known as charge density waves. Of the many structures that strongly-interacting electrons can form, it is unclear which are related to the superconductivity.

In this project, we take on this problem through a combination of experiments on materials that isolate key aspects of unconventional superconductivity, and calculations designed to predict properties of complex, correlated systems with guaranteed accuracy. We take advantage of the dramatic recent progress of precision numerical methods for correlated electron systems, in order to formulate specific conditions for achieving desired properties. These calculations will be validated by results from the experimental portion of this proposal, and in turn will generate hypotheses that are testable experimentally. The experimental method to be employed here is to apply extremely large pressures to samples, in order to distort their lattices. This method has proved to be very powerful: under high pressure, the electronic properties of many materials differ so much from the unpressurised material that they can be considered, in effect, as new materials. Our results will provide insight into the key conditions that favour robust superconductivity, and allow development of improved materials for applications such as in renewable energy and quantum computation.