Short-Range Order in VI3.

We present a detailed investigation of the crystal structure of VI3, a two-dimensional van der Waals material of interest for studies of low-dimensional magnetism. As opposed to the average crystal structure that features R3̅ symmetry of the unit cell, our Raman scattering and X-ray atomic pair distribution function analysis supported by density functional theory calculations point to the coexistence of short-range ordered P3̅1c and long-range ordered R3̅ phases. The highest-intensity peak, A1g3, exhibits a moderate asymmetry that might be traced back to the spin-phonon interactions, as in the case of CrI3.

Peculiar symmetry-protected electronic dispersions in two-dimensional materials.

Symmetry indicates that low energy spectra of materials could be richer than well-known Dirac, semi-Dirac, or quadratic, hosting some unusual quasiparticles. Performing the systematic study of exact forms of low energy effective Hamiltonians and dispersions in high-symmetry points with fourfold degeneracy of bands, we found new, previously unreported dispersion, which we named poppy flower after its shape. This massless fermion exists in non-magnetic two-dimensional (2D) crystals with spin-orbit coupling, which are invariant under one of the proposed ten noncentrosymmetric layer groups. We suggest real 3D layered materials suitable for exfoliation, having layers that belong to these symmetry groups as candidates for realization of poppy flower fermions. In 2D systems without spin-orbit interaction, fortune teller-like fermions were theoretically predicted, and afterward experimentally verified in the electronic structure of surface layer of silicon. Herein, we show that such fermions can also be hosted in 2D crystals with spin-orbit coupling, invariant under additional two noncentrosymmetric layer groups. This prediction is confirmed by density functional based calculation: layered BiIO4, which has been synthesized already as a 3D crystal, exfoliates to stable monolayer with symmetry pb2_1a, and fortune teller fermion is observed in the band structure. Analytically calculated density of states of the poppy flower shows semimetallic characteristic, in contrast to metallic nature of fortune teller having non-zero density of states at the bands contact energy. We indicate possibilities for symmetry breaking patterns which correspond to the robustness of the proposed dispersions as well as to the transition from Dirac centrosymmetric semimetal to poppy flower.