Broad boron sheets and boron nanotubes: An<i>ab initio</i>study of structural, electronic, and mechanical properties

Abstract

Based on a numerical ab initio study, we discuss a structure model for a broad boron sheet, which is the analog of a single graphite sheet, and the precursor of boron nanotubes. The sheet has linear chains of $sp$ hybridized $\ensuremath{\sigma}$ bonds lying only along its armchair direction, a high stiffness, and anisotropic bonds properties. The puckering of the sheet is explained as a mechanism to stabilize the $sp$ $\ensuremath{\sigma}$ bonds. The anisotropic bond properties of the boron sheet lead to a two-dimensional reference lattice structure, which is rectangular rather than triangular. As a consequence the chiral angles of related boron nanotubes range from 0\ifmmode^\circ\else\textdegree\fi{} to 90\ifmmode^\circ\else\textdegree\fi{}. Given the electronic properties of the boron sheets, we demonstrate that all of the related boron nanotubes are metallic, irrespective of their radius and chiral angle, and we also postulate the existence of helical currents in ideal chiral nanotubes. Furthermore, we show that the strain energy of boron nanotubes will depend on their radii, as well as on their chiral angles. This is a rather unique property among nanotubular systems, and it could be the basis of a different type of structure control within nanotechnology.