Vanishing edge currents in non-p-wave topological chiral superconductors

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The edge currents of two dimensional topological chiral superconductors with nonzero Cooper pair angular momentum---e.g., chiral p-, d-, and f-wave superconductivity---are studied. Bogoliubov-de Gennes and Ginzburg--Landau calculations are used to show that in the continuum limit, only chiral p-wave states have a nonzero edge current. Outside this limit, when lattice effects become important, edge currents in non-p-wave superconductors are comparatively smaller, but can be nonzero. Using Ginzburg--Landau theory, a simple criterion is derived for when edge currents vanish for non-p-wave chiral superconductivity on a lattice. The implications of our results for putative chiral superconductors such as Sr2RuO4 and UPt3 are discussed.