Novel vortex lattice transition in d-wave superconductors

TL;DR

This paper predicts a novel first-order transition in the vortex lattice structure of d-wave superconductors, from triangular to square, influenced by vortex interactions and anisotropy, with implications for high-temperature superconductors like YBCO.

Contribution

It introduces a new vortex lattice transition driven by fourfold modulation effects in the extended Ginzburg-Landau framework for d-wave superconductors.

Findings

Vortex acquires a fourfold modulation proportional to cos(4φ).

Attractive interaction between vortices aligned along specific directions.

First-order transition from triangular to square vortex lattice at a critical field.

Abstract

We study the vortex state in a magnetic field parallel to the $c$ axis in the framework of the extended Ginzburg Landau equation. We find the vortex acquires a fourfold modulation proportional to $\cos(4\phi)$ where $\phi$ is the angle ${\bf r}$ makes with the $a$-axis. This term gives rise to an attractive interaction between two vortices when they are aligned parallel to $(1,1,0)$ or $(1,-1,0)$. We predict the first order vortex lattice transition at $B=H_{cr}\sim \kappa^{-1} H_{c2}(t)$ from triangular into the square lattice tilted by $45^\circ$ from the $a$ axis. This gives the critical field $H_{cr}$ a few Tesla for YBCO and Bi2212 monocrystals at low temperatures ($T\leq 10 K$).