Vanishing edge currents in non-$p$-wave topological chiral superconductors

TL;DR

This paper investigates edge currents in 2D topological chiral superconductors, revealing that only chiral p-wave states sustain nonzero edge currents in the continuum limit, with lattice effects reducing or nullifying these currents.

Contribution

It demonstrates that non-p-wave chiral superconductors have vanishing or reduced edge currents due to lattice effects, providing a criterion for their presence or absence.

Findings

Only chiral p-wave states have nonzero edge currents in the continuum limit.

Lattice effects diminish or eliminate edge currents in non-p-wave superconductors.

A simple criterion is derived for when edge currents vanish on a lattice.

Abstract

The edge currents of two dimensional topological chiral superconductors with nonzero Cooper pair angular momentum---e.g., chiral $p$-, $d$-, and $f$-wave superconductivity---are studied. Bogoliubov-de Gennes and Ginzburg--Landau calculations are used to show that in the continuum limit, \emph{only} chiral $p$-wave states have a nonzero edge current. Outside this limit, when lattice effects become important, edge currents in non-$p$-wave superconductors are comparatively smaller, but can be nonzero. Using Ginzburg--Landau theory, a simple criterion is derived for when edge currents vanish for non-$p$-wave chiral superconductivity on a lattice. The implications of our results for putative chiral superconductors such as Sr2RuO4 and UPt3 are discussed.