Symmetry of rolled-up rectangular lattice nanotubes

Abstract

The high symmetry of a single-wall nanotube made of a rectangular lattice sheet rolled up into a cylinder is described by a line group. Such a tube is characterized by helical symmetry, while it has translational periodicity if the squares of a rectangular lattice vector are commensurate or if its chiral vector is orthogonal to a rectangular lattice vector. Possible additional symmetry elements are consequences of the non-translational symmetries of the layer (e.g.rotational axis and mirror planes). Except for a two-fold axis, they appear only if a chiral vector matches specific, rather restrictive, conditions. © 2006 IOP Publishing Ltd.