Coexistence of electronic and phononic type-II hourglass Weyl nodal rings in two-dimensional ultralight crystals

Abstract

Hourglass Weyl nodal rings (HWNRs), particularly their two-dimensional (2D) counterparts, have engendered considerable intrigue because of the unique band dispersion. However, because of the non-negligible spin–orbit coupling effect on the electronic band structures, the coexistence of electronic and phononic type-II HWNRs, which are jointly protected by a single-valued 2D irreducible representation and the nonsymmorphic symmetry, has been rarely explored in realistic 2D materials. In this work, based on first-principles calculations, we propose the MgBCl monolayer, an ultralight crystal material with high thermodynamic stability, as the first realistic material that hosts type-II HWNRs in electronic and phononic systems. Moreover, we further employ symmetry analysis to confirm the coexisting type-II HWNRs and show their clear edge states. Our work not only provides an effective platform for the experimental detection of the coexisting type-II HWNRs in spinless systems but also offers realistic materials for investigating the interplay between topological electronic and phononic states.