Vortex State in a d-Wave Superconductor

TL;DR

This paper explores the vortex state in d-wave superconductors using Ginzburg-Landau theory, revealing complex vortex structures, lattice shapes, and experimental signatures of d-wave symmetry.

Contribution

It introduces a detailed analysis of vortex structures and lattice configurations in d-wave superconductors, including novel predictions for experimental detection.

Findings

Isolated vortex has four symmetric nodes in s-wave component

Abrikosov lattice is generally oblique with shape depending on field and s-d mixing

Magnetic field distribution shows double peak line shape in experiments

Abstract

We discuss the physics of the vortex state in a $d$-wave superconductor, using the phenomenological Ginzburg-Landau theory, where many novel phenomena arise from the small admixture of the $s$-wave component induced by spatial variations in the dominant $d$-wave. Properties of an isolated vortex and of the Abrikosov vortex lattice are studied by means of analytic and numerical methods. An isolated vortex has a considerable structure, with four ``extra'' nodes in the $s$-wave order parameter symmerically placed around the core and an amplitude forming a four-lobe profile decaying as $1/r^2$ at large distances. The supercurrent and magnetic field distributions are also calculated. The Abrikosov lattice is in general oblique with the precise shape determined by the magnetic field and $s$-$d$ mixing parameter $\epsilon_v$. The magnetic field distribution in the Abrikosov state has two nonequivalent saddle points resulting in the prediction of a double peak line shape in $\mu$SR and NMR experiments as a test of a $d$-wave symmetry. Detailed comparison is made with existing experimental data and new experiments are proposed to test for the predicted effects.