Block spin magnetism and metal-insulator transition in a two-dimensional Hubbard model with perfect vacancy superstructure

TL;DR

This paper investigates how vacancy superstructures in a 2D Hubbard model influence magnetism and metal-insulator transitions, revealing intermediate magnetic metallic phases and their relevance to certain iron-based compounds.

Contribution

It provides an exact solution for the non-interacting case and explores the phase diagram, highlighting the effects of vacancies and interactions on magnetic and insulating states.

Findings

Mid-band gap opens at weak inter-block hopping.

Metal-insulator transition occurs before magnetic instability.

Intermediate magnetic metal phase emerges at moderate hopping.

Abstract

We study the phase diagram of a square lattice Hubbard model with a perfect vacancy superstructure. The model can be also defined on a new bipartite lattice with each building blocks consisting of a minimal square. The non-interacting model is exactly solved and a mid-band gap opens at the Fermi energy in the weak inter-block hopping regime. Increasing the Coulomb interaction will develop the N\'eel antiferromagnetic order with varying block spin moments. The metal-insulator transition with $U_{\rm MI}$ smaller than the one without vacancies occurs above the magnetic instability $U_{\rm M}$. The emergent intermediate magnetic metal phase develops substantially in the moderate inter-block hopping regime. Drastic increases in the ordered moment and gap magnitude on the verge of non-interacting band insulator signal a possible distinction between the magnetic semi-conductor and the Mott-insulator. The implications of these results for the recent discovered (A,Tl)$_{y}$Fe$_{2-x}$Se$_2$ compounds are discussed.