Current inversion at the edges of a chiral $\boldsymbol{p}$-wave superconductor

TL;DR

This paper investigates edge quasiparticle states in a chiral p-wave superconductor, revealing band filling effects on edge currents and states, with insights from Bogolyubov-de Gennes and Ginzburg-Landau theories.

Contribution

It provides a detailed analysis of edge states and currents in a topological chiral p-wave superconductor, highlighting band filling effects and comparing microscopic and phenomenological approaches.

Findings

Edge currents can flow in opposite directions depending on edge geometry and band filling.

Zero-energy bound states explain the reversed current flow.

Ginzburg-Landau theory reproduces the microscopic results.

Abstract

Motivated by Sr$_2$RuO$_4$, edge quasiparticle states are analyzed based on the self-consistent solution of the Bogolyubov-de Gennes equations for a topological chiral $p$-wave superconductor. Using a tight-binding model of a square lattice for the dominant $\gamma$-band we explore the non-trivial geometry and band structure dependence of the edge states and currents. As a peculiar finding we show that for high band fillings currents flow in reversed direction comparing straight and zigzag edges. We give a simple explanation in terms of the positions of the zero-energy bound states using a quasi-classical picture. We also show that a Ginzburg-Landau approach can reproduce these results. Moreover, the band filling dependence of the most stable domain wall structure is discussed.