Cat's cradle-like Dirac semimetals in layer groups with multiple screw axes: Application to 2D Borophene and Borophane

Recently, the crystal symmetry-protected topological semimetals have aroused extensive interests, especially for 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 novel cat's cradle-like topological semimetal phase, which looks like multiple hourglass-like band structures staggered together. Furthermore, we propose the monolayer borophene and borophane with pmmn layer group as the first material class to realize such novel semimetal phase. A pair of tilted anisotropic Dirac cones at the Fermi level is revealed in the two-dimensional boron-based materials and the low-energy effective models are given. Moreover, akin to three-dimensional Weyl semimetal, the topological property of these cat's cradle-like Dirac semimetals can be verified by the calculation of quantized Berry phase and the demonstration of 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.