Antiferromagnetic Chern insulator in centrosymmetric systems

TL;DR

This paper demonstrates the theoretical existence of an antiferromagnetic Chern insulator in a centrosymmetric square lattice model, expanding the understanding of AFCI states beyond noncentrosymmetric systems and suggesting potential for high-temperature quantum anomalous Hall applications.

Contribution

It introduces a new square lattice model with inversion symmetry that hosts an AFCI, showing its emergence due to spin-orbit coupling and electronic correlations, and highlights its potential for technological applications.

Findings

A collinear AFCI appears between band insulator and AF Mott insulator phases.

The AFCI state is stabilized by a large checkerboard potential.

Results suggest AFCI as a generic phenomenon beyond specific models or lattices.

Abstract

An antiferromagnetic Chern insulator (AFCI) can exist if the effect of the time-reversal transformation on the electronic state cannot be compensated by a space group operation. The AFCI state with collinear magnetic order is already realized in noncentrosymmetric honeycomb structures through the Kane-Mele-Hubbard model. In this paper, we demonstrate the existence of the collinear AFCI in a square lattice model which preserves the inversion symmetry. Our study relies on the time-reversal-invariant Harper-Hofstadter-Hubbard model extended by a next-nearest-neighbor hopping term including spin-orbit coupling and a checkerboard potential. We show that an easy $z$-axis AFCI appears between the band insulator at weak and the easy $xy$-plane AF Mott insulator at strong Hubbard repulsion provided the checkerboard potential is large enough. The close similarity between our results and the results obtained for the noncentrosymmetric Kane-Mele-Hubbard model suggests the AFCI as a generic consequence of spin-orbit coupling and strong electronic correlation which exists beyond a specific model or lattice structure. An AFCI with the electronic and the magnetic properties originating from the same strongly interacting electrons is promising candidate for a strong magnetic blue shift of the charge gap below the N\'eel temperature and for realizing the quantum anomalous Hall effect at higher temperatures so that applications for data processing become possible.