Vortex lattice structure in a d_{x^2-y^2}-wave superconductor

TL;DR

This paper studies the vortex lattice structure in a d_{x^2-y^2}-wave superconductor near the upper critical field, revealing temperature-dependent shape transitions and the influence of induced s-wave components using extended Ginzburg Landau theory.

Contribution

It extends the Ginzburg Landau framework to include higher order derivatives, analyzing vortex lattice shape, orientation, and symmetry in d-wave superconductors with and without induced s-wave order.

Findings

Vortex lattice shape transitions from triangular to square with decreasing temperature.

Orientation of the vortex lattice can align along the crystal axes.

Induced s-wave order parameter modifies the characteristic features of the vortex lattice.

Abstract

The vortex lattice structure in a d_{x^2-y^2}-wave superconductor is investigated near the upper critical magnetic field in the framework of the Ginzburg Landau theory extended by including the correction terms such as the higher order derivatives derived from the Gor'kov equation. On lowering temperature, the unit cell shape of the vortex lattice gradually varies from a regular triangular lattice to a square lattice through the shape of an isosceles triangle. As for the orientation of the vortex lattice, the base of an isosceles triangle is along the a axis or the b axis of the crystal. The fourfold symmetric structure around a vortex core is also studied in the vortex lattice case. It is noted that these characteristic features appear even in the case the induced s-wave order parameter is absent around the vortex of the d_{x^2-y^2}-wave superconductivity. We also investigate the effect of the induced s-wave order parameter. It enhances (suppresses) these characteristic features of the d_{x^2-y^2}-wave superconductor when the s-wave component of the interaction is attractive (repulsive).