Role of symmetry in antiferromagnetic topological insulators

In this investigation, we delve into the interplay between strong interactions and intricate topological configurations, leading to emergent quantum states such as magnetic topological insulators. The crux of our research centers on elucidating how lattice symmetry modulates antiferromagnetic quantum Hall phenomena. Utilizing the spinful Harper-Hofstadter model enriched with a next-nearest-neighbor (NNN) hopping term, we discern a half-filling bandgap, paving the way for the manifestation of a quantum Hall insulator characterized by a Chern number, C = 2. Upon integrating a checkerboard-patterned staggered potential (Δ) and the Hubbard interaction (U), the system exhibits complex dynamical behaviors. Marginal NNN hopping culminates in a Neél antiferromagnetic Mott insulator. In contrast, intensified hopping results in stripe antiferromagnetic configurations. Moreover, in the regime of limited NNN hopping, a C = 1 Neél antiferromagnetic quantum Hall insulator emerges. A salient observation pertains to the manifestation of a C = 1 antiferromagnetic quantum Hall insulator when spin-flip mechanisms are not offset by space group symmetries. These findings chart a pathway for further explorations into antiferromagnetic Quantum Hall States.