Inversion symmetry breaking induced triply degenerate points in orderly arranged PtSeTe family materials

k paths exactly with [Formula: see text] symmetry allow to find triply degenerate points (TDPs) in band structures. The paths that host the type-II Dirac points in PtSe₂ family materials also have the [Formula: see text] spatial symmetry. However, due to Kramers degeneracy (the systems have both inversion symmetry and time reversal symmetry), the crossing points in them are Dirac ones. In this work, based on symmetry analysis, first-principles calculations, and [Formula: see text] method, we predict that PtSe₂ family materials should undergo topological transitions if the inversion symmetry is broken, i.e. the Dirac fermions in PtSe₂ family materials split into TDPs in PtSeTe family materials (PtSSe, PtSeTe, and PdSeTe) with orderly arranged S/Se (Se/Te). It is different from the case in high-energy physics that breaking inversion symmetry I leads to the splitting of Dirac fermion into Weyl fermions. We also address a possible method to achieve the orderly arranged in PtSeTe family materials in experiments. Our study provides a real example that Dirac points transform into TDPs, and is helpful to investigate the topological transition between Dirac fermions and TDP fermions.

Large Positive Thermal Expansion and Small Band Gap in Double-ReO3-Type Compound NaSbF6

Double-ReO₃-type structure compound NaSbF₆ undergoes a low-temperature rhombohedral to high-temperature cubic phase between 303 and 323 K, as revealed by temperature-dependent X-ray diffractions. Although many double-ReO₃-type fluorides exhibit either low thermal expansion or negative thermal expansion (NTE), NaSbF₆ exhibits positive thermal expansion (PTE) with a large volumetric coefficient of thermal expansion, α_v = 62 ppm/K, in its cubic phase. Raman spectroscopy reveals that the low-frequency transverse vibration of fluorine atoms is stiffened in NaSbF₆, compared with the typical NTE compound CaZrF₆ with the same structure. The related weak contraction associated with the polyhedral rocking would be overcome by the notable elongation of the Na-F bond length on heating, thus leading to the large volumetric PTE. Unlike ScF₃ and CaZrF₆ which are insulators with a wide band gap, a relative small band gap of 3.76 eV was observed in NaSbF₆. The small band gap can be attributed to the hybridization between the Sb 5s and F 2p orbitals.

Edge-controlled half-metallic ferromagnetism and direct-gap semiconductivity in ZrS2 nanoribbons

Intrinsic half-metallic ferromagnetism and direct-gap semiconductivity are predicted in ZrS₂ nanoribbons with different edge configurations.