Vortex core states in a minimal two-band model for iron-based superconductors

TL;DR

This study uses a minimal two-band model to analyze vortex core states in iron-based superconductors, revealing how pairing symmetry influences local electronic structures and how magnetic order can suppress resonance states.

Contribution

It introduces a self-consistent two-band BdG framework to compare $d_{x^2-y^2}$-wave and $s_{x^2y^2}$-wave pairing effects on vortex core states in iron-based superconductors.

Findings

Resonance core states are bound in $d_{x^2-y^2}$-wave pairing.

Resonance states in $s_{x^2y^2}$-wave pairing can become extended with doping.

Antiferromagnetic order suppresses vortex core resonance states.

Abstract

The pairing symmetry is one of the major issues in the study of iron-based superconductors. We adopt a minimal two-band tight-binding model with various channels of pairing interaction, and derive a set of two-band Bogoliubov-de Gennes (BdG) equations. The BdG equations are implemented in real space and then solved self-consistently via exact diagonalization. In the uniform case, we find that the $d_{x^2-y^2}$-wave pairing state is most favorable for a nearest-neighbor pairing interaction while the $s_{x^2y^2}$-wave pairing state is most favorable for a next-nearest-neighbor pairing interaction. The is consistent with that reported by Seo {\em et al.} [Phys. Rev. Lett. {\bf 101}, 206404 (2008)]. We then proceed to study the local electronic structure around a magnetic vortex core for both $d_{x^2-y^2}$-wave and $s_{x^2y^2}$-wave pairing symmetry in the mixed state. It is found from the local density of states (LDOS) spectra and its spatial variation that the resonance core states near the Fermi energy for the $d_{x^2-y^2}$-wave pairing symmetry are bound while those for the $s_{x^2y^2}$-wave pairing symmetry can evolve from the localized states into extended ones with varying electron filling factor. Furthermore, by including an effective exchange interaction, the emergent antiferromagnetic spin-density-wave (SDW) order can suppress the resonance core states, which provides one possible avenue to understand the absence of resonance peak as revealed by recent scanning tunneling microscopy experiment (STM) by Yin {\em et al.} [Phys. Rev. Lett. {\bf 102}, 097002 (2009)].