Temperature dependent gap anisotropy in Bi₂Sr₂CaCu₂O_8+x as evidence for a mixed-symmetry ground state

In a recent experiment, Ma et al. measured the temperature dependence of the gap anisotropy of oxygen-annealed Bi2Sr2CaCu2O8+x. Their measurements were taken along the two directions Gamma-M and Gamma-X. They found that the gap along both directions is nonzero at low temperatures and that the ratio of the two gaps is strongly temperature dependent. We show, using Ginzburg-Landau theory, that this behavior can be obtained if one assumes the existence of s-wave and d-wave components for the order parameter. Our theory predicts orthorhombic anisotropy in the gap, and a somewhat anomalous behavior for the electronic specific heat below T-c in this material. Since recent experiments indicate nearly pure d-wave symmetry for YBa2Cu3O7, this would imply that different high-T-c materials have substantially different order parameter symmetries.