An effective mean field theory for the coexistence of anti-ferromagnetism and superconductivity: Applications to iron-based superconductors and cold Bose-Fermi atomic mixtures

TL;DR

This paper develops an effective mean-field theory to analyze the coexistence of superconductivity and anti-ferromagnetism in electronic and cold atomic systems, revealing conditions favoring different pairing symmetries.

Contribution

It introduces a unified mean-field framework that accounts for both phenomena and their interactions mediated by spin fluctuations and BEC excitations.

Findings

Coexistence of superconductivity and anti-ferromagnetism is possible in the models.

Spin fluctuations favor d-wave superconductivity.

BEC excitations favor s-wave superconductivity.

Abstract

We study an effective fermion model on a square lattice to investigate the cooperation and competition of superconductivity and anti-ferromagnetism. In addition to particle tunneling and on-site interaction, a bosonic excitation mediated attractive interaction is also included in the model. We assume that the attractive interaction is mediated by spin fluctuations and excitations of Bose-Einstein condensation (BEC) in electronic systems and Bose-Fermi mixtures on optical lattices, respectively. Using an effective mean-field theory to treat both superconductivity and anti-ferromagnetism at equal footing, we study the model within the Landau energy functional approach and a linearized theory. Within our approaches, we find possible co-existence of superconductivity and anti-ferromagnetism for both electronic and cold-atomic models. Our linearized theory shows while spin fluctuations favor d-wave superconductivity and BEC excitations favor s-wave superconductivity.