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 ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and ${\mathrm{UPt}}_3$ are discussed.

• Received 1 October 2014
• Revised 5 December 2014

DOI:https://doi.org/10.1103/PhysRevB.90.224519