Structural and electronic properties of coiled and curled carbon nanotubes having a large number of pentagon--heptagon pairs

A family of Haeckelite nanotubes is generated by rolling up a two-dimensional threefold coordinated carbon network composed of pentagon-heptagon pairs and hexagons in proportion 2:3. The corresponding two-dimensional network is highly strained due to the presence of adjacent pentagons and heptagons. When the sheet is folded into a cylinder, part of the strain is released by having the pentagons protrude outward, and sometimes inward the tube. Due to that property, a large variety of structures can be generated such as coiled, screwlike, curled, and pearl-necklace-like nanotubes. All the Haeckelite nanotubes obtained in this work are semiconductors, some having a small band gap. Scanning-tunneling microscopy images, computed for a few Haeckelite nanotubes, show salient topographic protrusions at the location of the pentagon pairs.