Suppression of spontaneous supercurrents in a chiral p-wave superconductor

The superconducting state of strontium ruthenate (SRO) is widely believed to have chiral p-wave order that breaks time-reversal symmetry. Such a state is expected to have a spontaneous magnetization, both at sample edges and at domain walls between regions of different chirality. Indeed, muon spin-resonance experiments are interpreted as evidence of spontaneous magnetization due to domain walls or defects in the bulk. However, recent magnetic-microscopy experiments place upper limits on the magnetic fields at the sample edge and surface which are as much as 2 orders of magnitude smaller than the fields predicted theoretically for a somewhat idealized chiral p-wave superconductor. We investigate the effects on the spontaneous supercurrents and magnetization of rough and pair-breaking surfaces for a range of parameters within a Ginzburg-Landau formalism. The effects of competing orders nucleated at the surface are also considered. We find the conditions under which the edge currents are significantly reduced while leaving the bulk domain-wall currents intact, are quite limited. The implications for interpreting the existing body of experimental results on superconducting SRO within a chiral p-wave model are discussed.