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

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 Sr sub(2)RuO sub(4) and UPt sub(3) are discussed.