Electronic band dispersion of vertically aligned multiwall-carbon nanotubes (original) (raw)
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Electronic band structure of carbon nanotubes
2005
Here |a 1 | = |a 2 |= a 0 = √3a CC where a CC is the bonding distance of the two adjacent carbon atom and is equal to 0.142nm and m > n. Having been familiar with chiral vector, its usage and its relationship with unit vectors a 1 and a 2 , one can investigate the geometry of carbon nanotube.
Physical Review B, 2010
Narrow diameter tubes and especially (6,5) tubes with a diameter of 0.75 nm are currently one of the most studied carbon nanotubes because their unique optical and especially luminescence response makes them exceptionally suited for biomedical applications. Here we report on a detailed analysis of the electronic structure of nanotubes with (6,5) and (6,4) chiralities using a combined experimental and theoretical approach. From high-energy spectroscopy involving x-ray absorption and photoemission spectroscopy the detailed valence- and conduction-band response of these narrow diameter tubes is studied. The observed electronic structure is in sound agreement with state of the art ab initio calculations using density-functional theory.
Bandstructure Effects in Multiwall Carbon Nanotubes
We report conductance measurements on multiwall carbon nanotubes in a perpendicular magnetic field. A gate electrode with large capacitance is used to considerably vary the nanotube Fermi level. This enables us to search for signatures of the unique electronic band structure of the nanotubes in the regime of diffusive quantum transport. We find an unusual quenching of the magnetoconductance and the zero bias anomaly in the differential conductance at certain gate voltages, which can be linked to the onset of quasi-one-dimensional subbands.
Band theory and electronic structures of carbon nanotubes
Synthetic Metals, 1997
A band structure model for carbon nanotubes taking into account the deformation potential characterizing the conformal mapping of graphene to tubules is presented and overlap is introduced in theT band calculations. This model corresponds to the study of aone-dimensional ( ID) system and is not simply the limit of a 2D system becoming quasi-1D. While development is explicitly made for the zigzag tubules, the method itself can also be applied to the armchair and chiral configurations by modifying the structure factor and boundary conditions. 0 1997 Elsevier Science S.A.
2013
Optical dispersion spectra at energies up to 30 eV play a vital role in understanding the chirality-dependent van der Waals London dispersion interactions of single wall carbon nanotubes (SWCNTs). We use one-electron theory based calculations to obtain the band structures and the frequency dependent dielectric response function from 0-30 eV for 64 SWCNTs differing in radius, electronic structure classification, and geometry. The resulting optical dispersion properties can be categorized over three distinct energy intervals (M, π, and σ, respectively representing 0-0.1, 0.1-5, and 5-30 eV regions) and over radii above or below the zone-folding limit of 0.7 nm. While π peaks vary systematically with radius for a given electronic structure type, σ peaks are independent of tube radius above the zone folding limit and depend entirely on SWCNT geometry. We also observe the so-called metal paradox, where a SWCNT has a metallic band structure and continuous density of states through the Fermi level but still behaves optically like a material with a large optical band gap between M and π regions. This paradox appears to be unique to armchair and large diameter zigzag nanotubes. Based on these calculated one-electron dielectric response functions we compute and review Van der Waals -London dispersion spectra, full spectral Hamaker coefficients, and van der Waals -London dispersion interaction energies for all calculated frequency dependent dielectric response functions. Our results are categorized using a new optical dielectric function classification scheme that groups the nanotubes according to observable trends and notable features (e.g. the metal paradox ) in the 0-30 eV part of the optical dispersion spectra. While the trends in these spectra begin to break down at the zone folding diameter limit, the trends in the related van der Waals -London dispersion spectra tend to remain stable all the way down to the smallest single wall carbon nanotubes in a given class.
Electronic Band Structure of Coiled Carbon Nanotubes
Acta Physica Polonica A, 2011
More than fifteen years have passed since the first report of experimental evidence of regularly coiled carbon nanotubes, but, the structure, formation mechanism and theoretical aspects of these nanotubes still remain unresolved. We propose model of hexagonal, helically coiled single wall carbon nanotubes, determine their line group symmetry and calculate electronic band structure of the relaxed configurations by means of fully symmetry adopted density functional tight binding method implemented into the POLSym code. Electrical properties of the straight and coiled carbon nanotubes of different chiralities are compared and analyzed.
Calculation of the band structure of a non-chiral semiconductor and metallic carbon nanotubes
Journal of physics, 2018
A new form of the linear augmented cylindrical wave method is proposed. For the construction of basis functions, the electron potential is taken to be spherically symmetric in atomic regions, constant in the intermediate region and cylindrically symmetric in the vacuum regions. The basis functions of the method, obtained from the solution of the Schrodinger equation in the corresponding domains, are sewn on the boundaries of the MT-spheres and the cylindrical surfaces of the tube, forming everywhere continuous and differentiable functions. In order to approve a method, the band structure of the non-chiral semiconductor and metallic single-wall carbon nanotubes was calculated.
On the basis of density functional theory, we study the electronic structures of (3,3), (4,4), (5, 0) and (6, 0) SWCNTs. The results show that the cohesive energy of armchair tubes are larger than those of zigzag ones. The calculated band gap of (4,4) is smaller than those of other tubes. Moreover, the band gap for armchair tubes are smaller than those of zigzag. The variation of ionization potential, electron affinity, and Fermi energy level as the number of atoms in the tube grows up. This curve fluctuates strongly because of the change in size that produce different surfaces with different properties. The IP is larger than the EA, as is the normal situation for molecules. The highest number of degenerate states in the conduction and valence bands are about as follow: 7, 9, 9, and 7 for (3,3), (4,4), (5,0) and (6,0) CNTs, respectively.
Chirality correlation in double-wall carbon nanotubes as studied by electron diffraction
Physical Review B, 2006
Structural correlation between two adjacent graphitic layers in double-wall carbon nanotubes ͑DWNTs͒ was systematically examined by using electron diffraction. Chiral angles and tube diameters were carefully measured, and the chiral indices of individual DWNTs were accurately determined. As a result, it was found that the interlayer distances of DWNTs were widely distributed in the range between 0.34 and 0.38 nm. Chiralities of the inner and outer tubes tended to be distributed at higher chiral angles, approaching 30°, for the tubes with diameter D Ͻ ϳ 3 nm. On the other hand, for the tubes with D Ͼ ϳ 3 nm, the chiral angles were widely distributed, covering the chiral map entirely. Therefore, we consider that tubes with small diameters have a tendency to form armchair type. Correlation of chiralities between the inner and outer tubes was found to be random.