Recently, the crystal symmetry-protected topological semimetals have aroused extensive interest, especially the nonsymmorphic symmetry-protected one. We list the possible nonmagnetic topological semimetals and develop their $k·p$ Hamiltonian in all layer groups with multiple screw axes in the absence of spin-orbital coupling. We find a cat's-cradle-like topological semimetal phase which looks like multiple hourglasslike band structures staggered together. Furthermore, we propose monolayer borophene and borophane with the $pmmn$ layer group as the first material class to realize such a semimetal phase. A pair of tilted anisotropic Dirac cones at the Fermi level is revealed in two-dimensional boron-based materials, and the low-energy effective models are given. Moreover, akin to a three-dimensional Weyl semimetal, the topological property of these cat's-cradle-like Dirac semimetals can be verified by the calculation of a quantized Berry phase and the demonstration of a flat Fermi-arc edge state connecting two Dirac points as well. Our finding that borophene and borophane are cat's-cradle-like Dirac semimetals is of great interest for experiment and possible applications in the future.

• Received 22 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.195437