Three-dimensional borophene: A light-element topological nodal-line semimetal with direction-dependent type-II Weyl fermions

Abstract

Since spin can be regarded as a dummy degree of freedom, light-element topological semimetals (TSMs) are expected to be a promising alternative for spin-orbit-coupling based TSMs, which usually contain costly and toxic heavy elements. Using first-principles calculations combined with a bottom-up assembly strategy, herein we identify an intriguing light-element TSM, termed 3D borophene, which can be obtained by stacking synthesized 2D triangular borophene along the perpendicular direction. Under the protection of mirror symmetry, the linear band crossings between $\mathrm{B}\ensuremath{-}{p}_{xz}$ and ${p}_{y}$ states in the vicinity of the Fermi energy form two Weyl nodal lines running across the Brillouin zone in the ${k}_{y}=0$ plane. When the nodal lines are projected on the (010) surface, drumheadlike surface states and open Fermi arcs are observed, which provide vital evidence for experimental identification. Remarkably, by examining the defined slope index of the crossing bands in all possible $\mathbit{k}$ paths, we find that the nodal lines of 3D borophene are composed of type-II Weyl points due to the emergence of tilted Weyl cones. Our findings not only establish a lightweight Weyl-nodal-line semimetal, but also highlight a bottom-up assembly strategy for designing desirable TSMs from synthetic 2D materials.