Spontaneous Edge Current in Chiral Superconductors with High Chirality

Abstract

We study the spontaneous edge current of chiral superconductors with high chirality both in the absence and presence of Meissner screening. We compute the edge current from a self-consistent solution to a set of coupled equations: quasiclassical Eilenberger equation, superconducting gap equation, and Maxwell equation. We find that the spatial dependent chiral edge current is largely suppressed and has more nodes for higher chirality pairings. In the absence of Meissner screening, the integrated current at T=0 is zero for all higher chirality pairings; while it is substantial for chiral p-wave. This conclusion is consistent with previous studies. In contrast, at finite T, the integrated current is non-zero even for higher chiral pairings. It turns out that the spatial varying order parameter is crucial to understand this finite T behavior of the edge current. When Meissner screening is included, the magnitude of the edge currents is reduced for all chiral pairings; however, the reduction is much weaker in higher chirality cases. We conclude that the Meissner effect is not that important for higher chiral pairings. We also consider the effect of the rough surface on the edge current. The edge current of even chiral pairings is inverted by the strong surface roughness; however, that of the odd chiral pairings is not. The sub-dominant order parameters, induced by the surface, are the key to understanding this current inversion.