Renormalization group approach to anisotropic superconductors at finite temperature

TL;DR

This paper develops a renormalization group method for analyzing anisotropic superconductors at finite temperature, extending previous approaches and clarifying the relationship with mean-field theory, with applications to high-Tc cuprates.

Contribution

It introduces a finite-temperature RG approach for anisotropic superconductors, generalizing existing methods and providing a scale-invariant gap equation framework.

Findings

RG effectively describes critical behavior in anisotropic superconductors

The gap function at criticality is a single eigenfunction of the interaction kernel

Model predictions align with experimental data on high-Tc cuprates

Abstract

A renormalization group (RG) analysis of the superconductive instability of an anisotropic fermionic system is developed at a finite temperature. The method appears a natural generalization of Shankar's approach to interacting fermions and of Weinberg's discussion about anisotropic superconductors at T=0. The need of such an extension is fully justified by the effectiveness of the RG at the critical point. Moreover the relationship between the RG and a mean-field approach is clarified, and a scale-invariant gap equation is discussed at a renormalization level in terms of the eigenfunctions of the interaction potential, regarded as the kernel of an integral operator on the Fermi surface. At the critical point, the gap function is expressed by a single eigenfunction and no symmetry mixing is allowed. As an illustration of the method we discuss an anisotropic tight-binding model for some classes of high $T_c$ cuprate superconductors, exhibiting a layered structure. Some indications on the nature of the pairing interaction emerge from a comparison of the model predictions with the experimental data.