Non-topological nature of the edge current in a chiral p-wave superconductor

TL;DR

This paper investigates the non-topological nature of edge currents in chiral p-wave superconductors, showing they are sensitive to microscopic details and can be reduced by anisotropy, unlike topologically protected Majorana modes.

Contribution

The study provides a comprehensive theoretical analysis demonstrating that edge currents in chiral p-wave superconductors are non-topological and sensitive to microscopic details, contrasting with the topological Majorana states.

Findings

Edge currents are not quantized and are sensitive to microscopic details.

Edge currents can be substantially reduced by anisotropic gap functions.

Majorana bound states are topologically robust, unlike edge charge currents.

Abstract

The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological--and therefore sensitive to microscopic details--even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr$_2$RuO$_4$.