Antiferromagnetic Chern insulator in centrosymmetric systems
Morad Ebrahimkhas, Götz S. Uhrig, Walter Hofstetter, Mohsen Hafez-Torbati
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 a promising candidate for a strong magnetic blueshift 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.