Microscopic Derivation of the Ginzburg-Landau Equations for a d-wave Superconductor

TL;DR

This paper derives Ginzburg-Landau equations for d-wave superconductors from microscopic lattice models, analyzing how their coefficients vary with physical parameters and exploring implications for vortex lattice experiments.

Contribution

It provides a microscopic derivation of GL equations for d-wave superconductors from two lattice models, including numerical analysis of coefficient variations and higher-order anisotropic terms.

Findings

Coefficients vary with carrier density, temperature, and coupling constants.

Higher-order anisotropic terms influence vortex lattice structures.

Analytical results align with continuum models at low densities.

Abstract

The Ginzburg-Landau (GL) equations for a d-wave superconductor are derived within the context of two microscopic lattice models used to describe the cuprates: the extended Hubbard model and the Antiferromagnetic-van Hove model. Both models have pairing on nearest-neighbour links, consistent with theories for d-wave superconductivity mediated by spin fluctuations. Analytical results obtained for the extended Hubbard model at low electron densities and weak-coupling are compared to results reported previously for a d-wave superconductor in the continuum. The variation of the coefficients in the GL equations with carrier density, temperature, and coupling constants are calculated numerically for both models. The relative importance of anisotropic higher-order terms in the GL free energy is investigated, and the implications for experimental observations of the vortex lattice are considered.