Nontopological nature of the edge current in a chiral p-wave superconductor

The edges of time-reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are nontopological—and therefore sensitive to microscopic details—even if we neglect Meissner screening. We give insight into the nontopological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov–de Gennes equations, the quasiclassical approximation, and the gradient expansion, and we describe those special cases in which edge currents do have a topological character. While edge currents are not quantized, they are generically large, but they can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr2RuO4.