Structure of vortex-bound states in spin-singlet chiral superconductors

TL;DR

This paper analyzes vortex-bound states in spin-singlet chiral superconductors, revealing zero-energy Majorana flat bands in certain pairing symmetries and providing spectroscopic signatures to identify the order parameter symmetry.

Contribution

It provides a detailed theoretical study of vortex-bound states in different chiral pairing symmetries using exact diagonalization and analytical methods.

Findings

Zero-energy Majorana flat bands in ($d_{xz} \\pm i d_{yz}$)-wave vortices

Finite-energy vortex-bound states in ($d_{x^2-y^2} \\pm i d_{xy}$)-wave superconductors

Distinct tunneling conductance signatures for vortices and antivortices

Abstract

We investigate the structure of vortex-bound states in spin-singlet chiral superconductors with ($d_{x^2-y^2} \pm i d_{xy}$)-wave and ($d_{xz} \pm id_{yz}$)-wave pairing symmetries. It is found that vortices in the ($d_{xz} \pm id_{yz}$)-wave state bind zero-energy states which are dispersionless along the vortex line, forming a doubly degenerate Majorana flat band. Vortex-bound states of ($d_{x^2-y^2} \pm i d_{xy}$)-wave superconductors, on the other hand, exist only at finite energy. Using exact diagonalization and analytical solutions of tight-binding Bogoliubov-de Gennes Hamiltonians, we compute the energy spectrum of the vortex-bound states and the local density of states around the vortex and antivortex cores. We find that the tunneling conductance peak of the vortex is considerably broader than that of the antivortex. This difference can be used as a direct signature of the chiral order parameter symmetry.