Helium-3 B phase ($A_B=\Delta R,R^{T}R=I,\det R=1$)

Take a proper rotation matrix $R$ with real number entries. Then ${\mathbf{d}}_B=\Delta R\hat{\mathbf{k}}$ hasThis odd linear orbital model has an isotropic gap magnitude. Isotropic gap magnitude does not require s-wave pairing: the spin components can rotate together with the orbital direction. Nor does the magnitude fix the relative spin-orbit orientation represented by $R$.

For both displayed models, $\mathbf{d}\times {\mathbf{d}}^{\ast }=0$. The triplet gap matrix $\hat{\Delta }=(\mathbf{d}\cdot \mathbf{\sigma })i{\sigma }_y$, written with Pauli matrices, satisfiesThus these models give the same gap magnitude for the two spin branches. That last simplification would fail for a general complex triplet vector with a nonzero cross product. The displayed angular curves illustrate these specified matrices; they are not a microscopic derivation of the phase diagram.