Sub-gap in the Edge States of 2-D Chiral Superconductor with Rough Surface

TL;DR

This paper investigates how atomic-scale surface roughness affects the surface states and currents in a 2D chiral superconductor, revealing a sub-gap formation due to surface-bulk state interactions.

Contribution

It introduces a random S matrix model to analyze rough surface effects on chiral superconductors, highlighting the emergence of a sub-gap in surface states.

Findings

Surface mass current is suppressed by roughness.

A sub-gap appears between surface bound states and bulk states with diffusive surfaces.

Surface density of states resembles that of superfluid helium-3 B phase.

Abstract

We discuss the rough surface effects on a two-dimensional chiral $k_x+ik_y$ superconductor. The atomic scale roughness at the surface is considered using the random $S$ matrix model. The roughness effects on the self-consistent order parameter, the surface mass current and the surface density of states are studied using the quasi-classical theory. We find that the surface mass current is suppressed by the surface roughness. The surface density of states shows a quite similar behavior to that of superfluid ${}^3$He B phase. When the surface is specular, the surface Andreev bound states form a band which fills the bulk energy gap $\Delta_{\rm bulk}$. When the surface becomes diffusive, there occurs a sharp upper edge of the surface bound states band and there opens a sub-gap between the edge and the bulk energy gap. We show that this sub-gap is induced by the repulsion between the surface bound states and the propagating Bogoliubov quasi-particles through the second order process of roughness.