Lattice symmetry and emergence of antiferromagnetic quantum Hall states

Abstract

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 (QHI). The QHI 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 ∆ along the x-direction favoring a normal insulator (NI) and the Hubbard interaction U favoring a Mott insulator (MI). The MI is a Néel antiferromagnet (AF) for small and a stripe AF for large NNN hopping. We investigate the U -∆ 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 QHI (AFQHI) in the phase diagram, there is no equivalent C = 1 Néel AFQHI at the small NNN hopping. We discuss that a C = 1 AFQHI can emerge only if the effect of the spin-flip transformation cannot be compensated by a space group operation.