Impurity resonance peaks in the vortex core of cuprate superconductors with induced spin density wave order

Abstract

Considering the competing spin density wave (SDW) and $d$-wave superconductivity interactions, we investigate the effects of a nonmagnetic impurity on the vortex-core state of cuprate superconductors within the Bogoliubov--de Gennes formalism. We illustrate that the local SDW order is induced by the impurity on top of the magnetic field induced SDW order. The local density of states of a pinned vortex core exhibit a resonance peak at negative energy, which is drastically different from the double-peak structure observed in an unpinned vortex core. This resonance peak is insensitive to the impurity-scattering strength. Consequently, the impurity resonance peak may be used to identify the nature of vortex-core state of cuprate superconductors.