| Over twenty years after their discovery, the cuprate superconductors are still a source of interest and excitement. In addition to their unusually high superconducting transition temperature, these material display a rich variety of puzzling phenomena, such as a highly anomalous "normal" (non-superconducting) state, and an interplay between superconductivity and several other types of order, including spin, charge, and possibly more exotic types of order. In this thesis, I study some of the properties of the cuprates that make them so special. I show that the enigmatic "Fermi arcs", which are disconnected Fermi surfaces that appear in angle-resolved photoemission experiments in the normal state, can originate from strong superconducting fluctuations above the critical temperature. I give a short overview of the "competing orders" for which there is evidence in the cuprates, and show how the existence or absence of nodal quasiparticle excitations at low temperature can be used to identify them. Finally, I discuss recent experiments on a particular subset of the cupate family, in which there is evidence for a new state which combines charge, spin and superconducting orders in a unique way. All these unusual properties are argued to be related to the strong electron-electron interactions in these materials. |
