Based on first-principles calculations, we present various properties of single- and double-layered boron sheets, along with single- and double-walled boron nanotubes. Single-layered boron sheets, made of hexagons and triangles, have buckled ground-state geometries if the ratio of triangles to hexagons is large and stay flat otherwise. We demonstrate that this asymmetric behavior of buckling cannot be explained by a simple chemical picture based on $\sigma \text{−}\pi$ mixing. Instead, reduction in the electronic kinetic energy is the driving force for buckling. In addition, we show that double-layered boron sheets can form strong interlayer bonds between two layers only if the precursor single-layered sheet itself prefers a buckled ground-state structure. The optimal double-layered boron sheet in our library is semiconducting and is more stable than any single-layered sheet. Next, we discuss the curvature energies, buckling behavior and soliton structural fluctuations for single-walled boron nanotubes and the implications for the electronic properties of these nanotubes: our main finding is that the semiconducting nature of small-diameter single-walled nanotubes is robust under various perturbations and fluctuations. We end by showing that due to strong bonds forming between walls, the optimal double-walled boron nanotubes have different wall structures from single-walled ones. Such double-walled nanotubes are always more stable than any single-walled nanotube and are furthermore metallic for the likely experimentally relevant diameter range. We conclude with the implications of these results for fabricated nanotube systems.

• Received 30 April 2010

DOI:https://doi.org/10.1103/PhysRevB.82.115412