Abstract
We determine the mean-field ground state of the three-dimensional rotationally symmetric $d$-wave $(\ensuremath{\ell}=2)$ superconductor at weak coupling. It is a noninert state, invariant under the symmetry ${C}_{2}$ only, which breaks time-reversal symmetry almost maximally, and features a high but again less-than-maximal average magnetization. The state obtained by minimization of the expanded sixth-order Ginzburg--Landau free energy is found to be an excellent approximation to the true ground state. The coupling to a parasitic $s$-wave component has only a minuscule quantitative and no qualitative effect on the ground state.
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