Quasiparticles of d-wave superconductors in finite magnetic fields

TL;DR

This study investigates quasiparticles in d-wave superconductors within vortex lattices using self-consistent solutions of the Bogoliubov-de Gennes equations, revealing large dispersion of low-energy bands and tunneling conductance features consistent with experiments.

Contribution

It provides a detailed analysis of quasiparticle behavior in d-wave superconductors under magnetic fields, including the effects on tunneling spectra and the gradual mixing of order parameter components.

Findings

Low-energy quasiparticle bands have large dispersion even at low fields.

Tunneling conductance at vortex cores shows a double-peak structure near zero bias.

Mixing of other order parameter components develops gradually with increasing field.

Abstract

We study quasiparticles of d-wave superconductors in the vortex lattice by self-consistently solving the Bogoliubov-de Gennes equations. It is found for a pure $d_{x^2-y^2}$ state that: (i) low-energy quasiparticle bands in the magnetic Brillouin zone have rather large dispersion even in low magnetic fields, indicating absense of bound states for an isolated vortex; (ii) in finite fields with $k_F \xi_0$ small, the calculated tunneling conductance at the vortex core shows a double-peak structure near zero bias, as qualitatively consistent with the STM experiment by Maggio-Aprile et al. [Phys. Rev. Lett. {\bf 75} (1995) 2754]. We also find that mixing of a $d_{xy}$- or an s-wave component, if any, develops gradually without transitions as the field is increased, having little effect on the tunneling spectra.