The Electron Pairing of K$_x$Fe$_{2-y}$Se$_2$

TL;DR

This study investigates the pairing mechanisms in K$_x$Fe$_{2-y}$Se$_2$ using a two-stage functional renormalization group approach, revealing dominant nodeless $d_{x^2-y^2}$ pairing symmetry and the significance of buried hole bands.

Contribution

It introduces a detailed FRG analysis of K$_x$Fe$_{2-y}$Se$_2$, highlighting the role of buried hole bands and proposing a $J_1-J_2$ model for low-energy interactions.

Findings

Leading pairing symmetry is nodeless $d_{x^2-y^2}$.

Buried hole bands influence effective interactions.

Superconductivity described by a $J_1-J_2$ model.

Abstract

We studied the pairing instabilities in K$_x$Fe$_{2-y}$Se$_2$ using a two stage functional renormalization group (FRG) method. Our results suggest the leading and subleading pairing symmetries are nodeless $d_{x^2-y^2}$ and nodal extended $s$ respectively. In addition, despite having no Fermi surfaces we find the buried hole bands make important contributions to the final effective interaction. From the bandstructure, spin susceptibility and the FRG results we conclude that the low energy effective interaction in K$_x$Fe$_{2-y}$Se$_2$ is well described by a $J_1-J_2$ model with dominant nearest-neighbor antiferromagnetic interaction $J_1$ (at least as far as the superconducting pairing is concerned). In the end we briefly mention several obvious experiments to test whether the pairing symmetry is indeed $d_{x^2-y^2}$.