Dirac Cones and Nodal Line in Borophene.

Two-dimensional single-layer boron (borophene) has emerged as a new material with several intriguing properties. Recently, the β12 polymorph of borophene was grown on Ag(111), and observed to host Dirac fermions. Similar to graphene, β12 borophene can be described as atom-vacancy pseudoalloy on a closed-packed triangular lattice; however, unlike graphene, the origin of its Dirac fermions  is yet unclear. Here, using first-principles calculations, we probe the origin of Dirac fermions in freestanding and Ag(111)-supported β12 borophene. The freestanding β12 sheet hosts two Dirac cones and a topologically nontrivial Dirac nodal line with interesting Dirac-like edge states. On Ag(111), the Dirac cones develop a gap, whereas the topologically protected nodal line remains intact, and its position in the Brillouin zone matches that of the Dirac-like electronic states seen in the experiment. The presence of nontrivial topological states near the Fermi level in borophene makes its electronic properties important for both fundamental and applied research.