Nonanalytic supercurrents inHe3−A

The energy gap of the $A$ phase of superfluid ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ has two singular points on the Fermi surface. These singular points lead to various theoretical puzzles, including one recently discovered by Volovik and Mineev. These authors, using a generalized—gauge-transformation approximation, find a term in the $T=0\mathrm{}$ supercurrent which is nonanalytic in gradients of the order parameter. We use the quasiclassical equations invented by Eilenberger to check the validity of their approximation; we find that the generalized—gauge-transformation approximation fails, in that terms it leaves out make important (in fact, divergent) contributions to the nonanalytic supercurrent. We then formulate a new way to calculate the leading nonanalytic terms in the supercurrent.