Symmetry of the order parameter for high-temperature superconductivity

Whatever its microscopic origins, it seems likely that the superconductivity in the copper-oxides can be described by an appropriate Ginzburg-Landau theory. The possible order parameters and free energies are then determined by the symmetry breaking of the phase transition alone. The group-theoretically allowed states are enumerated here for singlet and triplet superconductors in orthorhombic and tetragonal crystals. As well as broken gauge, time reversal and rotational symmetries, broken translational symmetry states are also investigated. Experiments that might distinguish the various possible states are reviewed, concentrating especially on experiments where the outcomes are determined by the symmetry properties of the order parameter alone. These include Josephson effects, transition splitting, spontaneous strain and magnetism, critical and Gaussian fluctuations, collective modes and vortices. Current experimental results on the high-Tc materials are discussed where relevant, although in many cases these must be regarded as provisional.