Cohesive band structure of carbon nanotubes for applications in quantum transport

Abstract

An integrated cohesive band structure of carbon nanotubes (CNTs) applicable to all chirality directions (n, m), starting from the Dirac cone of a graphene nanolayer in k-space, is demarcated, in direct contrast to dissimilar chiral and achiral versions in the published literature. The electron wave state of a CNT is quantized into one-dimensional (1-D) nanostructure with a wrapping mode, satisfying the boundary conditions from one Dirac K-point to an equivalent neighboring one with an identical phase and returning to the same K point. The repetitive rotation for an identical configuration with added band index (n − m)mod3, yields one metallic (M) with zero bandgap corresponding to (n − m)mod3 = 0, semiconducting state SC1 with (n − m)mod3 = 1 and SC2 with (n − m)mod3 = 2. The band gap and effective mass of SC2 state are twice as large as those of SC1 state. A broad-spectrum expression signifying the linear dependence of the effective mass on the bandgap is obtained. Both the Fermi energy and the intrinsic velocity limiting the current to the saturation level is calculated as a function of the carrier concentration. Limitations of the parabolic approximation are pointed out. Several new features of the band structure are acquired in a seamlessly unified mode for all CNTs, making it suitable for all-encompassing applications. Applications of the theory to high-field transport are advocated with an example of a metallic CNT, in agreement with experimental observations. The mechanism behind the breakdown of the linear current–voltage relation of Ohm's law and the associated surge in resistance are explained on the basis of the nonequilibrium Arora's distribution function (NEADF). These results are important for the performance evaluation and characterization of a variety of applications on CNT in modern nanoscale circuits and devices.