Correlated Topological Phases in Altermagnets

We study the emergence of altermagnetic, correlated topological phases from repulsive interactions for electrons on the Lieb lattice. We establish that a quantum spin Hall effect can co-exist with altermagnetic spin order over a wide region of the parameter space for average electron densities of 2 and 4 per unit cell. We consider both non-interacting as well as interacting origins of this topological phase and explore how the magnetic structure along edges influences the electronic behavior of the associated topological edge modes. Finally, we study the robustness of these phases against inversion-symmetry breaking terms and disorder.