Anomalous chirality dependence of strain energy in gold nanotubes

A recent experiment reports the creation of goldene, which is two-dimensional gold with a hexagonal structure. By rolling up the goldene, gold nanotubes (GNTs) should exist, but their structural and electronic properties are not well understood. Based on first-principles calculations, we demonstrate a breakdown of the inverse square law, wherein the strain energy stored in a GNT decreases with the inverse square of the GNT radius. This is due to the enhanced strain energy in specific GNTs. The specific chiralities are identified by imposing the Bloch and geometric boundary conditions to the electronic structure of goldene having a hexagonal shape of the Fermi surface. We also confirm that the electronic states on the Fermi surface exhibit an in-plane character. These factors result in an increase in the strain energy.