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As the most prevalent element on our planet, carbon manifests a wide variety of allotropic phases, significantly contributing to its complex physical properties. Recently, several carbon allotropes have been reported to possess abundant topological phases in theory and experiment. This work focuses on a sp3 carbon allotrope, Z-ACA allotrope, which consists of 5-6-7-type Z-ACA carbon rings. This allotrope has been reported previously as a superhard material comparable to diamond. In this study, we report that it is a candidate for both an obstructed atomic insulator and a real Chern insulator. It is worth mentioning that Z-ACA exhibits an unconventional bulk-boundary correspondence due to its hinge boundary state manifestation. Our current research indicates that Z-ACA is a suitable carbon phase platform for studying the real topology and second-order bulk-boundary correspondence.

Two-dimensional (2D) nonmagnetic second-order topological insulators (SOTIs) have been exhaustively studied, whereas 2D magnetic SOTIs have received little attention from researchers. In this work, we have demonstrated using first-principles calculations that the 2D NiZrI6 monolayer is a 2D magnetic SOTI with a ferromagnetic ground state. Two spin channels in the 2D NiZrI6 monolayer exhibit nontrivial gaps. According to the higher-order bulk-boundary correspondence, the 2D NiZrI6 monolayer shows topologically protected corner states with quantized fractional charge (e/3) that are spin-polarized and pinned at the sample's corners in real space. In addition, the zero-dimensional corner states of the 2D NiZrI6 monolayer are resistant to spin–orbit coupling (SOC) effects. It is anticipated that 2D NiZrI6 monolayer with magnetic higher-order topology will contribute to topo-spintronics advancement.

Researchers are interested in magnetic topological materials because they can integrate magnetic and topological properties. Using the first-principles calculations, we identify the P6322-type SrNiIO6 as a dynamically stable half-metallic candidate with a completely spin-polarized Weyl complex formed by two hourglass charge-3 and six charge-1 Weyl points. Furthermore, distinct surface arcs linked the projections of two spin-polarized charge-3 Weyl points and six spin-polarized charge-1 Weyl points, resulting in a fully spin-polarized sextuple-helicoid surface arc mode on the (001) surface of P6322-type SrNiIO6. P6322-type SrNiIO6 with fully spin-polarized charge-3 and charge-1 Weyl points and a fully spin-polarized sextuple-helicoid surface arc mode is, without a doubt, a promising candidate for applications in spintronic and topological physics.

Exploration of topological phonons in two-dimensional (2D) has long been regarded as one of the central topics in topological physics. Due to their distinct band dispersion, hourglass nodal rings have garnered considerable attention, but their existence in 2D materials, particularly in spinless phonon systems, has received scant attention. Using the first-principle calculations, this study shows that P4/nmm type LiHS monolayer is an ideal candidate for hosting hourglass nodal ring phonons. Moreover, the phononic edge states induced by the nodal ring phonons in LiHS are also exhibited in this work. Our work provides the first 2D material candidate to study hourglass nodal ring phonons and the phononic edge states induced by the nodal ring phonons.