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

Abstract

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...

Excitons in metallic carbon nanotubes with Aharonov-Bohm flux

“…Energy bands of a ͑9,0͒ zigzag tube were previously calculated in a local-density approximation with many-body correction in a GW approximation. 59 In the absence of the many-body correction, the band gap after geometry relaxation is 0.12 eV, and the many-body correction enhances it by 40% to 0.17 eV. The present calculation gives much larger enhancement of factor 2 ϳ 2.5 for 0.1 Ͻ ͑e 2 / L͒͑2␥ / L͒ −1 Ͻ 0.2, as shown in Fig.…”

Enhanced static approximation to the electron self-energy operator for efficient calculation of quasiparticle energies

“…Subsequently GW calculations have been employed as a firstprinciples method for a broad array of real materials, 6-8 the physical systems ranging from bulk semiconductors 13 to nanoclusters [14][15][16] and nanotubes. 17,18 As the field has advanced, the methodology has been extended to include approximate self-consistency in the Green's function [19][20][21][22] and the role of vertex corrections is currently under debate, [23][24][25] both at the expense of further computational burden.…”

The effect of surface curvature of aluminum nitride nanotubes on the adsorption of NH3

“…Interestingly, this trend is in contrast to that of semiconducting CNTs. It has already been showed that the band gap of semiconducting CNTs inversely depends on the nanotube diameter [31,32]. It is known that the change of E g influences the nanotube reactivity.…”