CNT Bands Learning Materials

by Denis Areshkin

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By completing the CNTBands, you will be able to:

a) understand the relationship between system geometry (roll vector of nano-tube or crystallographic direction of nano-ribbon) and its band structure.

b) Understand the importance of employing screw symmetry in calculations of electronic properties of nano-tubes (Homework problems and solutions).

The specific objectives of the CNT-Bands are:

CNTBands-Scheme_Small.png

Recommended Reading

  • Key electronic properties of carbon nanotubes – a brief introduction
  • C.T. White, D.H. Roberrtson, and J.W. Mintmire, “Helical and rotational symmetries of nanoscale graphitic tubules”, PRB v. 47, p.5485 (1993)
  • D.A. Areshkin, D. Gunlycke, C.T. White, “Ballistic Transport in Graphene Nanostrips in the Presence of Disorder: Importance of Edge Effects”, NANO LETTERS v.7, p.204 (2007)
  • D.A. Areshkin, B.K. Nikolic, “I-V curve signatures of nonequilibrium-driven band gap collapse in magnetically ordered zigzag graphene nanoribbon two-terminal devices”, PRB v.79, 205430 (2009)

Demo

CNTBands : First Time User Guide

Tool Verification

Verification of the Validity of the CNTBands Tool

CNT

It is important to have a quantitative model describing how an interaction of the CNT with its environment (e.g. supporting substrate, other nanotubes, polymer matrix, etc.) influences CNT ability to conduct current. Localization length is the convenient measure of the robustness of CNT conductance with respect to random disorder. The localization length of a randomly distorted CNT is defined as its length, for which the logarithm of the ratio of ideal transmission to the transmission in the distorted CNT equals 2. The “Challenge Problem” explains how to relate the statistical dispersion of random disorder to the CNT localization length.

In the figure below blue curve is given by analytical expression for localization length. The simulated localization length, which has been statistically averaged over an ensemble of 750 randomly distorted CNTs is plotted in green color. Localization length is measured in numbers of CNT’s unit cells. The unit cell is defined as a minimum size unit cell, which interacts only with its nearest neighbors. Red line is the transmission of the ideal (undistorted) CNT in arbitrary units.

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Key Properties of Graphene Nano-Ribbons

Graphene – Geometry dependent band gap – Disorder-induced mobility gap in A-GNRs – Spin polarization along the edges in Z-GNRs – The possibility to remove spin polarization, and hence to reduce spin-induced band gap in Z-GNRs by passing current. – Simple computational models suggest that Z-GNR 60° turns are highly reflective and 120° are virtually transparent. These computations, however, do not include spin-polarization effect. Therefore, if the effect will be observed experimentally, the transmis-sion differences between 60° and 120° turns is expected to be less pronounced.

Intra-valley vs. Inter-valley Scattering in Z-GNRs

GNR Challenge Problem

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