Effective tight-binding model for the iron vacancy ordered A$_{y}$Fe$%_{1.6}$Se$_{2}$

TL;DR

This paper develops an effective tight-binding model for K$_{y}$Fe$_{1.6}$Se$_{2}$ that captures its electronic structure and magnetic instabilities, providing insights into its superconducting mechanism.

Contribution

The paper constructs a symmetry-preserving two-dimensional tight-binding model including vacancy order, revealing magnetic tendencies consistent with experiments and highlighting the role of spin fluctuations in superconductivity.

Findings

Block-checkerboard antiferromagnetism is favored at large Hund's coupling.

The model reproduces experimental magnetic instabilities.

Spin fluctuations at ($\pi$, $\pi$) are significant for superconductivity.

Abstract

We investigate the electronic structure of the ternary iron selenide K$_{y}$% Fe$_{1.6}$Se$_{2}$ by considering the spatial symmetry of the $\sqrt{5}% \times \sqrt{5}$ vacancy ordered structure. Based on three orbitals of $% t_{2g}$, which are believed to play major physics in iron-based superconductors, an effective two-dimensional tight binding Hamiltonian is constructed with the vacancy ordered structure being explicitly included. It is shown that the constructed band model, when combined with generalized Hubbard interactions, yields a spin susceptibility which exhibits both the block-checkerboard antiferromagnetism instability and the stripe antiferromagnetism instability. In particular, for large Hund's rule couplings, the block-checkerboard antiferromagnetism wins over the stripe antiferromagnetism, in agreement with the observation in experiments. We argue that such a model with correct symmetry and Fermi surface structures should be the starting point to model K$_{y}$Fe$_{1.6}$Se$_{2}$. The spin fluctuations at $\mathbf{q}$=($\pi ,\pi $) suggest that interblock fluctuations of spins might play an important role in the mechanism of superconductivity occurring in this system.