From quantum matter to high-temperature superconductivity in copper oxides

A review of the phases of copper oxides (especially the ‘strange metal’), discussing their high-temperature superconductivity and their various forms of quantum matter, and the implications for fundamental theory. Since the discovery of high temperature copper oxide superconductors nearly thirty years ago, much has been learned about the nature of the superconducting state and the novel forms of quantum matter involved. This Review concentrates on the related issues that have not been resolved, notably the complexity of the phase diagram for the copper oxides, and the simplicity and insensitivity to material details of the 'normal' state at elevated temperatures. The discovery of high-temperature superconductivity in the copper oxides in 1986 triggered a huge amount of innovative scientific inquiry. In the almost three decades since, much has been learned about the novel forms of quantum matter that are exhibited in these strongly correlated electron systems. A qualitative understanding of the nature of the superconducting state itself has been achieved. However, unresolved issues include the astonishing complexity of the phase diagram, the unprecedented prominence of various forms of collective fluctuations, and the simplicity and insensitivity to material details of the ‘normal’ state at elevated temperatures.