Altermagnetism and its induced higher-order topology on the Lieb lattice

Altermagnetism (AM) has brought renewed attention to the Lieb lattice. Here, we broaden the scope of altermagnetic models on the Lieb lattice by using a general scheme based on spin clusters. We design various altermagnetic models with d- and g-wave on the Lieb lattice, and investigate its interplay with spin-orbit coupling. While the altermagnetic unit cell reconstructs the topological edge states in the strip geometry and leads to the emergence of Dirac points, the in-plane magnetic moments of AM can induce gaps at these points. In an open square geometry, corner modes emerge within these gaps, realizing higher-order topological states. We further verify that the induction of higher-order topology is applicable to all altermagnetic configurations constructed here on the Lieb lattice, and is most pronounced for AM by comparing with the other types of magnetism such as ferromagnetism and ferrimagnetism. Our results highlight the exotic properties of AM, and suggest its potential applications in engineering topological quantum states.