Coherence Effects of Caroli-de Gennes-Matricon Modes in Nodal Topological Superconductors

TL;DR

This paper investigates how impurity scattering affects Caroli-de Gennes-Matricon modes in vortex states of nodal topological superconductors, revealing topological invariants influence coherence effects and zero-energy mode behavior.

Contribution

It analytically derives eigenvalues and eigenfunctions of CdGM modes in nodal topological superconductors and explores impurity effects linked to topological invariants.

Findings

Coherence factors vanish for zero-energy modes in certain momentum ranges due to topology.

Impurity effects are governed by the eigenfunctions and topological invariants.

Topological number influences the coherence effects of vortex core states.

Abstract

Coherence effects by the impurity scattering of Caroli--de Gennes--Matricon (CdGM) modes in a vortex for nodal topological superconductors have been studied. The coherence effects reflect a topological number defined on a particular momentum space avoiding the superconducting gap nodes. First, we analytically derived the eigenvalue and eigenfunction of the CdGM modes, including the zero-energy modes, in a nodal topological superconducting state without impurities, where we focused on a possible superconducting state of UPt$_3$ as an example. Then, we studied impurity effects on the CdGM modes by introducing the impurity self-energy, which are dominated by the coherence factor depending on the eigenfunction of the CdGM modes. For the zero-energy CdGM modes, the coherence factor vanishes in a certain momentum range, which is guaranteed by topological invariance characterized by the one-dimensional winding number.