[[Image(Title_Picture_v.02_Small.jpg, link=http://nanohub.org/site/wiki/523/Title_Picture_v.02.jpg)]]

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 ([/topics/CNTBandsProblems Homework problems and solutions]).



The specific objectives of the CNT-Bands are: 

[[Image(CNTBands-Scheme_Small.png, link=http://nanohub.org/site/wiki/523/CNTBands-Scheme.png)]]



== Recommended Reading ==

 * [/topics/KeyPropertiesCNT {{{[1]}}}] Key electronic properties of carbon nanotubes - a brief introduction

 * [http://prl.aps.org/abstract/PRL/v68/i5/p631_1 {{{[2]}}}]  C.T. White, D.H. Roberrtson, and J.W. Mintmire, “Helical and rotational symmetries of nanoscale graphitic tubules”, PRB v. 47, p.5485 (1993)

 * [http://pubs.acs.org/doi/abs/10.1021/nl062132h {{{[3]}}}]  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)

 * [http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.4467v2.pdf {{{[4]}}}]  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)

 * [/topics/KeyPropertiesGNR {{{[5]}}}] Key electronic properties of graphene nano-ribbons - a brief introduction

 * [/topics/ScatteringZGNR  {{{[6]}}}] Simple pictorial explanation of the difference between intra-valley and inter-valley scattering in zigzag-edge graphene nano-ribbons.  

== Demo ==

CNTBands : [http://nanohub.org/resources/6909 First Time User Guide] 


== Tool Verification ==

[/topics/CNTBandsVerify Verification of the Validity of the CNTBands Tool]


== [/topics/CNTBandsChallengeProblem  Solve the Challenge: 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 [/topics/CNTBandsChallengeProblem  "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.

[[Image(Fig_9_1110_Localization_Length_One_Channel_01.png,50%)]]

== Exercises and Homework Assignments ==

 * [/topics/CNTBandsProblems CNT homework problems with solutions] - 4 low-to-medium difficulty problems explaining the importance of screw symmetry utilization for CNT modeling.

 * [/topics/ScatteringZGNR  Intra-valley vs. Inter-valley Scattering in Z-GNRs] - 1 problem with solution 


== [/topics/GNRChallenge  Solve the Challenge: GNR] ==