Self-consistent electronic structure of a $d_{x^2-y^2}$ and a $d_{x^2-y^2}+id_{xy}$ vortex

TL;DR

This paper studies quasiparticle states in vortex cores of d-wave superconductors, revealing no bound states in pure d-wave cases and proposing a magnetic-field-induced mixed state to explain experimental observations.

Contribution

It introduces a self-consistent analysis of vortex states in d-wave superconductors and suggests a magnetic-field-induced $d_{x^2-y^2}+id_{xy}$ state to reconcile theory with experiments.

Findings

Pure $d_{x^2-y^2}$ superconductor has no bound vortex core states.

Extended quasiparticle states dominate in the vortex core.

Magnetic-field-induced $d_{x^2-y^2}+id_{xy}$ state explains experimental data.

Abstract

We investigate quasiparticle states associated with an isolated vortex in a d-wave superconductor using a self-consistent Bogoliubov-de Gennes formalism. For a pure $d_{x^2-y^2}$ superconductor we find that there exist no bound states in the core; all the states are extended with continuous energy spectrum. This result is inconsistent with the existing experimental data on cuprates. We propose an explanation for this data in terms of a magnetic-field-induced $d_{x^2-y^2}+id_{xy}$ state recently invoked in connection with the thermal conductivity measurements on Bi$_2$Sr$_2$CaCu$_2$O$_8$.