Lattice symmetry and emergence of antiferromagnetic quantum Hall states

TL;DR

This paper explores how lattice symmetry influences the emergence of antiferromagnetic quantum Hall states in a modified Harper-Hofstadter model, revealing conditions under which certain topological magnetic phases can form.

Contribution

It demonstrates that a $ ext{C}=1$ antiferromagnetic quantum Hall state appears only under specific symmetry conditions, providing new insights into the interplay of interactions, lattice symmetry, and topological phases.

Findings

A $ ext{C}=2$ quantum Hall insulator exists at half-filling with NNN hopping.

A $ ext{C}=1$ stripe antiferromagnetic quantum Hall insulator appears at large NNN hopping.

No $ ext{C}=1$ Néel antiferromagnetic quantum Hall insulator is found at small NNN hopping.

Abstract

Strong local interaction in systems with non-trivial 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 $\mathcal{C}=2$ as both spin components are in the same quantum Hall state. We add to the system a staggered potential $\Delta$ along the $\hat{x}$-direction favoring a normal insulator and the Hubbard interaction $U$ favoring a Mott insulator. The Mott insulator is a N\'eel antiferromagnet for small 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 $\mathcal{C}=1$ stripe antiferromagnetic quantum Hall insulator in the phase diagram, there is no equivalent $\mathcal{C}=1$ N\'eel antiferromagnetic quantum Hall insulator at the small NNN hopping. We discuss that a $\mathcal{C}=1$ 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.