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We determine the mean-field ground state of the three-dimensionalrotationally symmetric d-wave ($\ell=2$) superconductor at weak coupling. It isa non-inert state, invariant under the symmetry $C_{2}$ only, which breaks timereversal symmetry almost maximally, and features a high, but again less thanmaximal average magnetization. The state obtained by minimization of theexpanded sixth-order Ginzburg--Landau free energy is found to be an excellentapproximation to the true ground state. The coupling to a parasitic s-wavecomponent has only a minuscule quantitative and no qualitative effect on theground state.

Ground state of the three-dimensional BCS d-wave superconductor