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 β polymorph of borophene was grown on Ag(111), and observed to host Dirac fermions. Similar to graphene, β 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 β borophene. The freestanding β 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.