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Temperature dependent gap anisotropy in Bi$_{2}$Sr$_{2}$CaCu$_{2}$ O$_{8+x}$ 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 Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+x}$. Their measurements were taken along the two directions $Γ- M$ and $Γ- X$. They found that the gap along both directions is nonzero at low temperatures and that the ratio 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 anomalous behavior for the electronic specific heat below T$_c$.