Lifetime of edge modes at rough surfaces of chiral superconductors

Abstract

We study the effect of diffuse surface scattering on the edge modes in two-dimensional chiral superconductors with time-reversal symmetry-breaking Cooper pairs, each carrying angular momentum mℏ (m=1,2,3,⋯). To elucidate the diffuse scattering effect, we formulate the inverse lifetime Γ=ℏ/τ corresponding to the broadening of the surface density of states (SDOS) for the edge mode. This derivation uses random S-matrix theory, which allows us to describe the surface effect in a unified way from the specular to the diffuse limit within the quasiclassical theory framework of superconductivity. We find that Γ in the chiral states with m≥2 is larger than that in the chiral p-wave state (m=1) because of the multiple edge mode branches in former superconducting states (the number of which equals m). Diffuse scattering between the different branches causes a significant broadening of SDOS. In contrast, the edge mode in the chiral p-wave state is robust to diffuse scattering because only a single edge mode branch exists. We also discuss SDOS at the diffuse limit, where the description in terms of Γ is not useful. The diffuse scattering effect on SDOS can be understood qualitatively in terms of destructive interference analogous to that caused by impurity scattering in unconventional superconductors.

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