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

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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.