Bend-induced insulating gap in carbon nanotubes

Chibotaru, Liviu F.; Bovin, SA; Ceulemans, Arnout

doi:10.1103/physrevb.66.161401

Cited by 20 publications

(22 citation statements)

References 23 publications

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“…The diameter dependence has been discussed theoretically before in the effective mass theory 26 and in the tight-binding approximation, 27 and E g ϰ d −2 was obtained. These previous works are complementary to ours in the sense that they are valid in the large-diameter region and semiquantitative.…”

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confidence: 97%

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18
Miyake
¹
,
Saito
²

2005
Phys. Rev. B
47
5
26
0
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We study the electronic structure of the carbon nanotube theoretically by the first-principles techniques using the local-density approximation ͑LDA͒ with the many-body correction in the GW approximation. We find that the ͑9,0͒ tube is gapful irrespective of naive expectation from the graphene band structure. All of thehybridization effect, lattice relaxation effect, and many-body effect due to electron interaction enhance the band gap, and the value is as large as 0.17 eV when taking into account all effects. For the ͑n ,0͒ nanotubes with n = 9, 12, 15, and 18, the LDA gap is found to range from 0.08 to 0.02 eV. These sizable gap values obtained by the most reliable methods to date shed light on the classification of carbon nanotubes by their electronic transport properties.Carbon nanotubes 1 have attracted interest partly because their variety of electronic properties can be utilized in electronic devices. One of the remarkable properties is that they are either metallic or semiconducting, depending on the diameter and helical arrangement. A simple -only tightbinding model predicts that the ͑n , m͒ nanotube is "metallic" when the n − m is a multiple of three, otherwise it is semiconducting. 2 This "1 / 3 rule" can be understood by starting with graphene band structure and imposing the appropriate boundary condition. Looking into the details of the band structure, however, most "metallic" tubes are not gapless, except armchair tubes ͑n − m =0͒. When n − m is divisible by three but nonzero, the nanotube is a narrow-gap semiconductor because of hybridization between and orbitals. 3 The effect is caused by curvature of the tube, therefore it is more remarkable at smaller diameter.The excitation energy associated with adding or removing an electron is a fundamental physical value. Especially, the minimum gap is the most important value for device applications. Some experiments have measured the fundamental gap as a function of tube diameter by combining scanningtunneling spectroscopy ͑STS͒ and scanning-tunneling microscopy ͑STM͒. 4,5 However, the samples used in the experiments were a mixture of different chiral indices, thus a direct comparison with theoretical calculation is not possible. Another problem is sizable experimental uncertainty, which prevents us from discussing gap value with the accuracy of Ͻ0.1 eV.Theoretically, the density-functional theory combined with the local density approximation ͑LDA͒ 6,7 is a conventional tool for the quantitative description of electronic structures without adjustable parameters. However, LDA has a well-known drawback; it underestimates the band gap of semiconductors and insulators. The GW approximation ͑GWA͒ 8 is a computationally much more expensive but feasible method to overcome this problem. 9,10 It has been applied to many materials during last two decades and turned out to give accurate band gap of bulk semiconductors. 11,12 The GW method was applied to carbon nanotubes and found that the many-body correction significantly opens band gaps compared to the LDA in smal...

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confidence: 97%

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18
Miyake
¹
,
Saito
²

2005
Phys. Rev. B
47
5
26
0
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“…On the other hand, as a result of additional curvature, two kinds of strain ͑both stretch and compression͒ coexist in a ring, and the magnitude of strain varies form the inner edge to the outer edge. When tubes become strained or bent, there will be bend-induced gap, 3,26,27 gap energy changes, 2,27,28 localized gap states, 29,30 and asymmetric change in electronic structure. 31 The changes in electronic structures will affect the intensities, profiles, and frequencies of Raman peaks of CNTs.…”

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confidence: 99%

Additional curvature-induced Raman splitting in carbon nanotube ring structures

Ren

et al. 2009

Phys. Rev. B

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In this paper, a diameter-dependent Raman G band splitting phenomenon in carbon nanotube ring structures is reported and analyzed. In Raman spectra of such structures, more modes became visible as the diameters of rings decrease, and the frequencies of these modes keep unchanged. We attribute this to the resonance condition changes caused by additional curvatures in rings. In this case, perpendicular polarized light would take more effect in rings than in straight tubes as the additional curvature increases, thus intensity enhancements for E 1 ͑E 1g ͒ and E 2 ͑E 2g ͒ modes are observed.

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“…when is large (22) where . The zigzag tube is described by the curved lattice vectors of and in the cylindrical coordinate system as shown in …”

Section: Energy Bands In Cylindrical Coordinatesmentioning

confidence: 99%

“…1 [17], which is a zigzag formation or an armchair configuration if wrapped up horizontally. However, this approach requires the approximation that the cell is planar since the carbon atoms of each hexagonal cell are not on the same plane and the effect of curvature on the cell has been analyzed [21], [22]. If the carbon atoms are assumed to be on the surface of the tube, the single-walled carbon nanotubes (SWCNTs) could be described by cylindrical coordinates as shown in Fig.…”

Section: Energy Bands In Cylindrical Coordinatesmentioning

confidence: 99%

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Band Theory of Single-Walled Carbon Nanotubes

Zhang

2005

IEEE Trans. Nanotechnology

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In this paper, a curvilinear coordinate system is used in space and in -space to study the energy band of single-walled carbon nanotubes wrapped at a helical angle. Using this method, a general function of the bandgap associated with the radius of the tube and the helical angle is derived based on the tight-binding theory. The three-dimensional hexagonal Brillouin zone of the tube is on the surface of cylinder in the -space. For two tubes with different diameters, there is a distance between the cylindrical Brillouin zones in the radial direction. The Brillouin zone varies with the radius of the tube and the number of cells on the circumference. For the metallic zigzag tubes, the bandgaps decrease discretely to zero at the corners of the Brillouin zones, and those corners are singular points of zero gaps. With the transformation of coordinates, the metallic zigzag type is proven to be equivalent to an armchair configuration. Electrical characteristics of the chiral effects are briefly highlighted.

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Bend-induced insulating gap in carbon nanotubes

Cited by 20 publications

References 23 publications

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18
Miyake
¹
,
Saito
²

2005
Phys. Rev. B
47
5
26
0
View full text Add to dashboard Cite

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18
Miyake
¹
,
Saito
²

2005
Phys. Rev. B
47
5
26
0
View full text Add to dashboard Cite

Additional curvature-induced Raman splitting in carbon nanotube ring structures

Band Theory of Single-Walled Carbon Nanotubes

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Bend-induced insulating gap in carbon nanotubes

Cited by 20 publications

References 23 publications

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18Miyake1, Saito2 2005Phys. Rev. B475260View full textAdd to dashboardCite

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18Miyake1, Saito2 2005Phys. Rev. B475260View full textAdd to dashboardCite

Additional curvature-induced Raman splitting in carbon nanotube ring structures

Band Theory of Single-Walled Carbon Nanotubes

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Product

Resources

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Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18
Miyake
¹
,
Saito
²

2005
Phys. Rev. B
47
5
26
0
View full text Add to dashboard Cite

Band-gap formation in(n,0)single-walled carbon nanotubes(n=9,12,15,18
Miyake
¹
,
Saito
²

2005
Phys. Rev. B
47
5
26
0
View full text Add to dashboard Cite