Non-ergodic dynamics and topological-sector fluctuations in layered high-temperature superconductors

At low enough temperatures, the constituent electrons of certain materials flow as a single body with zero electrical resistance. This is called superconductivity. The behaviour was first measured in solid mercury, which superconducts at around -270C and is therefore classed as a low-temperature superconductor. Certain copper-oxide-based materials, however, can superconduct at much higher temperatures: up to -130C. These materials therefore belong to the separate group known as high-temperature superconductors. This group of materials have extremely complex multi-layered crystal structures that are difficult to model, meaning that a theory of high-temperature superconductivity remains one of the major unsolved problems in condensed-matter physics.

At any given temperature, a superconductor will either be in its normal or superconducting state. Recent experiments on copper-oxide-based materials measured large fluctuations in their electrical resistances at the transition temperature between these two states. The large fluctuations are a result of the complex structures of the materials: a theoretical model for this phenomenon will therefore uncover details of these structures and drive the research community towards a complete theory of high-temperature superconductivity. This will lead to advances in the myriad engineering applications of superconductivity, which include superconductor-based quantum computing, magnetic resonance imaging, particle confinement in synchrotrons such as the Large Hadron Collider, plasma confinement in fusion reactors, and superconducting quantum interference devices used for high-precision magnetic measurements in medicine and further afield.

In the short term, this research will mostly impact academic researchers, but also the public through my continued commitment to public engagement and outreach. Descriptions of my research to young people facing socio-economic disadvantage inspires them to remain in STEM education, which will benefit both their lives and careers, and also the wider public through a better educated workforce and the pooling of talent from different demographics.

Further public engagement will also benefit the wider public more directly. We invest in scientific research to drive long-term economic growth, but equally important is the cultural enrichment of science and science education in creating a well-informed and inspired public. This improves the quality of life and creative output of those touched by enrichment, and also helps to create a workforce that is educated, highly skilled and inspired to improve. Society as a whole will therefore benefit from my research and public engagement as this fosters both the economic competitiveness of the UK and economic performance on a global level.

In the long term, this research will contribute to a theory of high-temperature superconductivity. It is of course too soon to tell if such a theory could lead to the engineering of room-temperature superconducting devices. If this were to prove to be the case, however, it is feasible that we could undergo an energy revolution in which we could generate clean energy and store and transport it with almost perfect efficiency. The project therefore also addresses both Energy Storage and Materials for Energy Applications. Superconductors may also lead to the first accessible quantum computer, which would constitute an information revolution. The high magnetic fields expelled by superconducting materials are currently used in magnetic resonance imaging, nuclear magnetic resonance, and particle accelerators such as the Large Hadron Collider. Superconducting Josephson junctions are used to form superconducting quantum interference devices (SQUIDs), which we can use for high-precision magnetic measurements in many different systems, from detecting neural activity in the brain and small magnetic fields in the heart, to oil prospecting, mineral exploration and even the detection of gravitational waves. New high-temperature superconducting devices could make all of these applications more cost effective, which will benefit industrial organisations such as Oxford Instruments and Siemens, and society as a whole as the applications become more widely available. The research will therefore also contribute to Quantum Physics for New Quantum Technologies.

Further to this, topological physics could lead to quantum technologies that we cannot currently predict, but it is again feasible that such devices may contribute to energy and information revolutions. Finally, irreversible Markov chain Monte Carlo algorithms may be the next big step change in the Bayesian modelling of large data sets in computational statistics. Big Data is becoming increasingly relevant in our data-driven world; such step changes could bring large-scale changes to our analysis of the ever-larger data sets to which we are gaining access. Properly regulated, this could vastly improve the quality of life of the human race by increasing the efficiency of everyday systems. The specific algorithms I propose also have applications in Soft Matter Physics and Biophysics, which are both rapidly growing fields of applied and fundamental science research.