Superconductivity and Competing Orders in High Tc Cuprates

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Superconductivity is a phenomenon that has the potential to radically transform applications of electrical power, from high-field magnets, to power transmission, motors and generators. Using superconducting materials can significantly reduce our energy usage and enable technologies, such as medical MRI scanners or nuclear fusion reactors. The key to fully realizing this potential is to develop materials which can be operated at high temperature and carry high currents. Although the discovery of new materials can be somewhat serendipitous, the search has been guided by our fundamental understanding of their physics. The the class of materials with the best current prospects for developing superconducting applications at high temperature are the cuprates, as these have the highest critical temperatures at ambient pressure. However for the cuprates, unlike conventional superconductors, there is as yet no consensus as to the physical mechanism which causes the superconductivity. Although cuprates have been studied for 30 years, recently there has been a step change in our understanding of these materials which has, in large part, been driven by experiments carried out using very high magnetic fields to suppress superconductivity and x-rays and neutrons to probe the collective charge and spin correlations. These developments have brought some clarity to the charge-doping versus temperature phase diagram of these materials and has gone some way to identifying the microscopic origin of the so-called pseudogap and charge density wave phases. Although it is known that these phases coexist and compete with the superconductivity, it is less clear whether fluctuations associated with these phases is the root cause of high temperature superconductivity or rather competes and reduces it.Here we plan to build on these recent developments, which are in turn coupled to major advances in available experimental facilities, such as resonant inelastic x-ray scattering (RIXS) and very high magnetic fields, to make major advances in our understanding of cuprate superconductors. In particular, we will use x-ray and neutron spectroscopies to study the evolution of the magnetic and charge fluctuations as different cuprate materials are tuned across their doping-temperature phase diagram, with particular emphasis on the emergence of the pseudogap and charge ordered phases. Another major new angle we will seek to exploit is the use of high pressure techniques in conjunction with high magnetic fields to measure quantum oscillations and magneto-transport properties. By forcing atoms together with pressure the properties are changed in ways that are different from charge doping. For example, it is only under high pressure that the highest transition temperatures of cuprates are realised. Pressure can be used to remove accidental degeneracies between competing phases and hence hopefully clarify which of these are important for superconductivity and which are not.