Ginzburg-Landau Theory for Flux Phase and Superconductivity in $t-J$ Model

TL;DR

This paper derives Ginzburg-Landau equations from the $t-J$ model to describe flux phase and superconductivity in high-$T_c$ cuprates, capturing microscopic electronic effects and enabling detailed analysis of surface, impurity, and magnetic field influences.

Contribution

It presents a microscopic derivation of GL theory from the $t-J$ model, incorporating electronic structure and Fermi surface effects for flux phase and superconductivity.

Findings

GL equations include flux phase and superconductivity with distinct couplings.

The theory predicts staggered currents for unidirectional flux phase variations.

Microscopic GL theory reflects doping-dependent electronic structures.

Abstract

Ginzburg-Landau (GL) equations and GL free energy for flux phase and superconductivity are derived microscopically from the $t-J$ model on a square lattice. Order parameter (OP) for the flux phase has direct coupling to a magnetic field, in contrast to the superconducting OP which has minimal coupling to a vector potential. Therefore, when the flux phase OP has unidirectional spatial variation, staggered currents would flow in a perpendicular direction. The derived GL theory can be used for various problems in high-$T_c$ cuprate superconductors, e.g., states near a surface or impurities, and the effect of an external magnetic field. Since the GL theory derived microscopically directly reflects the electronic structure of the system, e.g., the shape of the Fermi surface that changes with doping, it can provide more useful information than that from phenomenological GL theories.