Exploring connections between superconductivity, unconventional quantum order, and Fermi surface reconstruction

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We are in the midst of a materials revolution that is changing the face of technologies such as computation, solar energy, strong materials, and beyond.  Superconductivity has an important future role to play, in power generation and transmission, quantum computing, transportation, and magnet technology. This future, however,  depends on our ability to explore new materials systems, and to better understand unconventional superconductivity.  A huge advance in the physics of superconductors resulted from the discovery of heavy fermion, high-Tc copper-oxide, and iron-pnictide superconductors, but these discoveries revealed that there are deep physics issues that we don't understand, regarding the surprisingly intertwined physics of superconductivity, low-temperature magnetic phase transitions and, especially, Fermi surface reconstruction. The exploration of these issues has produced new and unexpected physics. My own research group, in our recent studies in this field, has been led into a broad range of topics: topological semi-metallic states in pyrochlore iridates, 'non-metallic metal' behaviour in frustrated magnetic metals, exotic quantum magnetism associated with Fermi surface transitions, and combined nuclear-electronic order parameters with a new kind of quantum critical point in praseodymium-based superconductors. At the same time we have added new experimental capabilities, so that we now have pressure cells that can reach 400 kilobar, and temperatures down to 10 mK, in magnetic fields up to 18 tesla. We use these to create novel states in complex matter.   Now we want to add new capabilities: the ability to apply very large uniaxial stress within a high-pressure volume; to use electronic structure calculations to guide our pressure or uniaxial stress measurements; and to use modern focussed-ion-beam sample preparation to rapidly and reliably prepare high-pressure measurements.  Such developments offer an excellent training ground for research students, and they will also allow us to advance rapidly. During this grant we will apply our capabilities to a variety of promising materials, as we also continue to work to understand recent discoveries in our group. An example of the former is Sr2RhO4, which is a cousin to high-temperature and topological superconductors. It has a distorted perovskite structure, and we will use electronic-structure calculations to understand how best to apply pressure to drive a very flat band, near the Fermi energy, across the Fermi energy, causing a major Fermi surface reconstruction and, I predict, superconductivity, perhaps even high temperature superconductivity.  An example of an ongoing project is a new collaboration with a group in the UK to explore combined nuclear-electronic order to below 1 millikelvin.  Our ultimate goal is new and improved superconducting technologies, but along the way there is a lot of new physics to explore.