Electronic properties of carbon nanotubes with distinct bond lengths

Abstract

In band structure calculations commonly used to derive the electronic properties of carbon nanotubes it is generally assumed that all bond lengths are equal. However, hexagonal carbon lattices are often irregular and may contain as many as three distinct bond lengths. A regular $(n,m)$ carbon nanotube will be metallic if p=(n-m)/3 for integer p. Here we analytically derive the generalized condition for metallic irregular carbon nanotubes. This condition is particularly relevant to small radius nanotubes and nanotubes experiencing small applied strains. In band structure calculations commonly used to derive the electronic properties of carbon nanotubes, it is generally assumed that all bond lengths are equal. However, hexagonal carbon lattices are often irregular and may contain as many as three distinct bond lengths. A regular ͑n , m͒ carbon nanotube will be metallic if p = ͑n − m͒ / 3 for integer p. Here we analytically derive the generalized condition for metallic irregular carbon nanotubes. This condition is particularly relevant to small radius nanotubes and nanotubes experiencing small applied strains.

Influence of Tension and Compression on the Band Structure of Carbon Nanotubes as Probed by the Cylindrical Wave Method

“…Let us consider the effect of axial deformations on the band structure of four chiral ((8,7), (9,6), (10,5), (12,1)) and four achiral ((7,7), (13,0), (12,0), (13,0)) nanotubes with roughly the same diameter ~10 Å but different geometry. Torsional amplitudes are limited to |Δh z | ≤ 5%, since the cylindrical geometry of nanotubes persists within these limits, while at higher amplitudes it is subjected to irreversible distortions [19][20][21][22][23]. The effect of torsional modes in the range |∆ω| ≤ 2 deg/Å on these tubes has been described in [15].…”

“…We have used the same method to study the response of the band structure of chiral and achiral nanotubes to torsional modes [15]. Previously, the effect of the response of the band structure of tubes has been studied using approximate analytical calculations in the framework of the π-electron theory and by the extended Hückel method [16][17][18][19][20][21][22][23]. Δh z…”