Lattice Symmetry And Emergence Of Antiferromagnetic Quantum Hall States

Strong local interaction in systems with nontrivial topological bands can stabilize quantum states such as magnetic topological insulators. We investigate the influence of the lattice symmetry on the possible emergence of antiferromagnetic quantum Hall states. We consider the spinful Harper-Hofstadter model extended by a next-nearest-neighbor (NNN) hopping which opens a gap at half filling and allows for the realization of a quantum Hall insulator. The quantum Hall insulator has the Chern number C = 2 as both spin components are in the same quantum Hall state. We add to the system a staggered potential Delta along the (x) over cap direction favoring a normal insulator and the Hubbard interaction U favoring a Mott insulator. The Mott insulator is a Ned antiferromagnet for small NNN hopping and a stripe antiferromagnet for large NNN hopping. We investigate the U-Delta phase diagram of the model for both small and large NNN hoppings. We show that, while for large NNN hopping there exists a C = 1 stripe antiferromagnetic quantum Hall insulator in the phase diagram, there is no equivalent C = 1 Neel antiferromagnetic quantum Hall insulator at the small NNN hopping. We discuss that a C = 1 antiferromagnetic quantum Hall insulator can emerge only if the effect of the spin-flip transformation cannot be compensated by a space-group operation. Our findings can be used as a guideline in future investigations searching for antiferromagnetic quantum Hall states.