Competing effective interactions of Dirac electrons in the Spin-Fermion system

TL;DR

This paper models Dirac electrons interacting with localized spins in a Spin-Fermion system, revealing multiple competing interactions such as superconductivity and magnetism, and explores their phase diagram through mean-field analysis.

Contribution

It introduces a unified framework to derive and analyze various effective interactions in a Dirac electron system coupled with localized spins.

Findings

Identification of multiple effective interactions including superconducting and magnetic terms.

Demonstration of the competition among different phases depending on system parameters.

Phase diagram mapping showing dominant interactions under various conditions.

Abstract

Recently discovered advanced materials, such as heavy fermions, frequently exhibit a rich phase diagram suggesting the presence of different competing interactions. A unified description of the origin of these multiple interactions, albeit very important for the comprehension of such materials is, in general not available. It would be therefore very useful to have a simple model where the common source of different interactions could be possibly traced back. In this work we consider a system consisting in a set of localized spins on a square lattice with antiferromagnetic nearest neighbors interactions and itinerant electrons, which are assumed to be Dirac-like and interact with the localized spins through a Kondo magnetic interaction. This system is conveniently described by the Spin-Fermion model, which we use in order to determine the effective interactions among the itinerant electrons. By integrating out the localized degrees of freedom we obtain a set of different interactions, which includes: a BCS-like superconducting term, a Nambu-Jona-Lasinio-like, excitonic term and a spin-spin magnetic term. The resulting phase diagram is investigated by evaluation of the mean-field free-energy as a function of the relevant order parameters. This shows the competition of the above interactions, depending on the temperature, chemical potential and coupling constants.