Realizing Corner States in Artificial Crystals Based on Topological Spin\n Textures

Abstract

The recent discovery of higher-order topological insulators (HOTIs) has\nsignificantly extended our understanding of topological phases of matter. Here,\nwe predict that second-order corner states can emerge in the dipolar-coupled\ndynamics of topological spin textures in two-dimensional artificial crystals.\nTaking a breathing honeycomb lattice of magnetic vortices as an example, we\nderive the full phase diagram of collective vortex gyrations and identify three\ntypes of corner states that have not been discovered before. We show that the\ntopological "zero-energy" corner modes are protected by a generalized chiral\nsymmetry in the sexpartite lattice, leading to particular robustness against\ndisorder and defects, although the conventional chiral symmetry of bipartite\nlattices is absent. We propose the use of the quantized $\\mathbb{Z}_{6}$ Berry\nphase to characterize the nontrivial topology. Interestingly, we observe corner\nstates at either obtuse-angled or acute-angled corners, depending on whether\nthe lattice boundary has an armchair or zigzag shape. Full micromagnetic\nsimulations confirm the theoretical predictions with good agreement.\nExperimentally, we suggest using the recently developed ultrafast Lorentz\nmicroscopy technique [M\\"{o}ller \\emph{et al}.,{arXiv:1907.04608}] to detect\nthe topological corner states by tracking the nanometer-scale vortex orbits in\na time-resolved manner. Our findings open up a promising route for realizing\nhigher-order topologically protected corner states in magnetic systems and\nfinally achieving topological spintronic memory and computing.\n