Spin–curvature interaction from curved Dirac equation: Application to single-wall carbon nanotubes

2017 ◽  
Vol 31 (15) ◽  
pp. 1750120
Author(s):  
Kai Zhang ◽  
Erhu Zhang ◽  
Huawei Chen ◽  
Shengli Zhang
Keyword(s):  
Carbon Nanotubes ◽  
Dirac Equation ◽  
Single Wall Carbon Nanotubes ◽  
Cylinder Surface ◽  
Effective Hamiltonian ◽  
Spinor Structure ◽  
Single Wall Carbon ◽  
Armchair Nanotubes ◽  
Energy Approximation ◽  
Analytical Expressions

The spin–curvature interaction (SCI) and its effects are investigated based on curved Dirac equation. Through the low-energy approximation of curved Dirac equation, the Hamiltonian of SCI is obtained and depends on the geometry and spinor structure of manifold. We find that the curvature can be considered as field strength and couples with spin through Zeeman-like term. Then, we use dimension reduction to derive the local Hamiltonian of SCI for cylinder surface, which implies that the effective Hamiltonian of single-wall carbon nanotubes results from the geometry and spinor structure of lattice and includes two types of interactions: one does not break any symmetries of the lattice and only shifts the Dirac points for all nanotubes, while the other one does and opens the gaps except for armchair nanotubes. At last, analytical expressions of the band gaps and the shifts of their positions induced by curvature are given for metallic nanotubes. These results agree well with experiments and can be verified experimentally.

Multiscale modelling of Carbon nanotubes

2003 ◽  
Vol 788 ◽  
Author(s):  
Marc Hamm ◽  
James A. Elliott ◽  
Huw J. Smithson ◽  
Alan H. Windle
Keyword(s):  
Carbon Nanotubes ◽  
Molecular Dynamics ◽  
Carbon Nanotube ◽  
Mode Analysis ◽  
Single Wall Carbon Nanotubes ◽  
Vibration Modes ◽  
Comprehensive Understanding ◽  
Single Wall Carbon ◽  
Long Wavelength ◽  
Armchair Nanotubes

ABSTRACTA comprehensive understanding of nanotube materials requires the ability to link different carbon nanotube models, which were developed to work at different length scales. Here we describe the mapping of a molecular dynamics (MD) model for single-wall carbon nanotubes onto a wormlike chain. This mapping employs a mode analysis of the bending fluctuations of the nanotube, similar to those used in experiments [1]. The essence of this mapping is to find an appropriate bending stiffness for the wormlike cha in in order to represent the nanotube on a coarsened scale. We find that this mapping will only work well, if the wavelength probing the nanotube stiffness is sufficiently large. For single-wall (9,9) armchair nanotubes vibration modes with node distances of 3 nm underestimate the long wavelength limit of the bending constant by about 50%. This mismatch tends to increase for tubes with larger radii.

Estimation of the mechanical properties of nanocomposites based on the properties prediction of single wall carbon nanotubes (SWCNT)

2015 ◽  
Vol 57 (5) ◽  
pp. 447-457 ◽  
Author(s):  
Hassan S. Hedia ◽  
Saad M. Aldousari ◽  
Ahmed K. Abdellatif ◽  
Gamal S. Abdelhaffez
Keyword(s):  
Mechanical Properties ◽  
Carbon Nanotubes ◽  
Single Wall Carbon Nanotubes ◽  
Single Wall Carbon

Confining H2 and D2 by adsorption in microporous carbons (single-wall carbon nanotubes and activated carbons) doped by K or Li

2005 ◽  
Vol 30 (4) ◽  
pp. 393-400 ◽  
Author(s):  
Szymon Los ◽  
Philippe Azais ◽  
Roland JM Pellenq ◽  
Yannick Breton ◽  
Olivier Isnard ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Activated Carbons ◽  
Single Wall Carbon Nanotubes ◽  
Single Wall Carbon ◽  
Microporous Carbons
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