Amorphous topological states, which are independent of the specific spatial distribution of microscopic constructions, have gained much attention. Recently, higher-order topological insulators, which are a new class of topological phases of matter, have been proposed in amorphous systems. Here, we propose a density-driven higher-order topological phase transition in a two-dimensional amorphous system. We demonstrate that the amorphous system hosts a topological trivial phase at low density. With an increase in the density of lattice sites, the topological trivial phase converts to a higher-order topological phase characterized by a quantized quadrupole moment and the existence of topological corner states. Furthermore, we confirm that the density-driven higher-order topological phase transition is size dependent. In addition, our results should be general and equally applicable to three-dimensional amorphous systems. Our findings may greatly enrich the study of higher-order topological states in amorphous systems.

The electronic structure shows that FAVI₃ is a novel organic–inorganic hybrid perovskite-type spin gapless semiconductor.

The structure, elasticity, and magnetic properties of Prussian blue analogue GaFe(CN)₆ under external pressure ranges from 0 to 40 GPa were studied by first principles calculations. In the range of pressure from 0 to 35 GPa, GaFe(CN)₆ not only has the half-metallic characteristics of 100% spin polarization, but also has stable mechanical properties. The external pressure has no obvious effect on the crystal structure and anisotropy of GaFe(CN)₆, but when the pressure exceeds 35 GPa, the half-metallicity of GaFe(CN)₆ disappears, the mechanical properties are no longer stable, and total magnetic moments per formula unit are no longer integer values.

The physical properties of two new quaternary Heusler alloys CoMnVSn and CoMnVSb were systematically studied by using first-principles calculation. The results show that the type-1 structures of ferromagnetic phase for these two alloys are the most stable. They all exhibit half-metallic behavior at equilibrium, and their half-metallic characteristics are maintained in the lattice region of 5.73–6.19 Å for CoMnVSn and 5.82–6.18 Å for CoMnVSb. The calculated magnetic moment M_t of each molecular unit in the half-metal lattice region strictly follows the Slater–Pauling empirical rule M_t = Z_t – 24, where Z_t is the number of valence electrons. The elastic constants show that the mechanical properties of the two compounds are stable at equilibrium, and the anisotropy factor and three-dimensional Young’s modulus confirm that they have anisotropy. It is expected that the CoMnVSn and CoMnVSb alloys are promising candidates in spintronics.