Surface Bound States and Spontaneous Edge Currents in Chiral Superconductors: Effect of Spatially Varying Order Parameter

We use the quasiclassical theory of superconductivity and examine the surface bound states and edge currents in two-dimensional chiral superconductors by focusing on the effect of spatially varying order parameter (OP). The chiral superconductivity is characterized by a two-component OP with symmetry of p + ip, d + id, etc. We consider the following situation, which occurs when the surface is assumed to be specular: one of the two OP components is significantly suppressed to zero at the surface and the other is enhanced from the bulk value near the surface. As a consequence of the OP suppression, bound-state modes (other than the so-called gapless mode) are generated at high energies close to the bulk gap. The contributions of the high-energy modes to the edge current density are as large as those of the gapless mode. However, in contrast to the gapless mode, the high-energy modes do not contribute to the total edge current Jtot. The OP enhancement near the surface leads to an unusual temperature dependence of Jtot as found by Wang et al. for non-p-wave chiral superconductors [Phys. Rev. B 98, 094501 (2018)].