Complete renormalization group calculation up to two-loop order of an effective two-band model for iron-based superconductors

TL;DR

This paper conducts a comprehensive two-loop renormalization group analysis of an effective two-band model for iron-based superconductors, assessing the robustness of previous one-loop results with higher-order quantum corrections.

Contribution

It provides the first complete two-loop RG calculation for this model, including self-energy effects and multiple susceptibilities, advancing understanding of quantum fluctuations in iron-based superconductors.

Findings

Two-loop corrections modify one-loop RG results significantly.

Self-energy effects influence the stability of superconducting and magnetic phases.

Higher-order quantum fluctuations are crucial for accurate low-energy descriptions.

Abstract

We perform a renormalization group (RG) study up to two-loop order of an effective low-energy two-band model to describe some of the recently discovered iron-based superconductors. Our starting point is the itinerant electronic model proposed by Chubukov \emph{et al.} [Phys. Rev. B \textbf{78}, 134512 (2008)], which displays two small, almost nested Fermi pockets with one hole pocket centered at $(0,0)$ and one electron pocket centered at $\mathbf{Q} = (\pi,\pi)$ in the folded Brillouin zone. We then proceed to implement a complete two-loop RG calculation for this model of four-point vertex corrections, quasiparticle weight and several order-parameter susceptibilities in order to evaluate the robustness of one-loop RG results available in the literature with respect to including self-energy effects and higher-order quantum fluctuations.