The construction of a carbon nanotube from a singlegraphene sheet and meaning of chiral angle. By rolling up the sheet along the wrapping vector C, that is, such that the origin (0,0) coincides with point C, a nanotube indicated by indices (11,7) is formed. Wrapping vectors along the dotted lines lead to tubes that are zigzag or armchair. All other wrapping angles lead to chiral tubes whose wrapping angle is specified relative to either the zigzag direction or to the armchair direction. Dashed lines are perpendicular to C and run in the direction of the tube axis indicated by vector T. The solid vector H is perpendicular to the armchair direction and specifies the direction of nearest-neighbour hexagon rows indicated by the black dots. The angle between T and H is the chiral angle. Carbon nanotubes can be thought of as graphitic sheets with a hexagonal lattice that have been wrapped up into a seamless cylinder. A carbon nanotube can be constructed by wrapping up a single sheet of graphite such that two equivalent sites of the hexagonal lattice coincide. The wrapping vector C, which defines the relative location of the two sites, is specified by a pair of integers (n,m) that relate C to the two unit vectors a1 and a2 (C = na1 + ma2). A tube is called ‘armchair’ if n equals m, and ‘zigzag’ in the case m = 0. All other tubes are of the ‘chiral’ type and have a finite wrapping angle lying between 0 and 30 deg.