First-Principles Calculation of the Electronic Properties of Single-Walled Carbon Nanotubes under Torsions
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First-Principles Calculation of the Electronic Properties of Single-Walled Carbon Nanotubes under Torsions K. Mihara and K. Shintani Department of Mechanical Engineering and Intelligent Systems, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu, Tokyo 182-8585, Japan ABSTRACT The structures and electronic properties of single-walled carbon nanotubes (SWNTs) under torsions are investigated using first-principles calculation based on the density functional theory. A SWNT of the chiral indices (5,0) is equilibrated under a torsion, and its equilibrium energy is obtained. It is revealed there is a structure having the minimum energy at a torsion of a specific angle of twist between 0 deg/Å and 1.88 deg/Å. Next, shear deformations corresponding to torsions imposed on the SWNTs of the chiral indices (5,0) and (5,1) are given to graphene sheets, and their energy band structures are calculated. It is concluded their band gaps decrease with the increase of the specific angle of twist. INTRODUCTION Carbon nanotubes (CNTs) can be metallic or semiconducting according to their chiralities. Since the discovery of CNTs [1], their applications to transistors and wires in electronic devices have been expected because of the large electron mobility in them. Their Young’s modulus is also so large that they may be used as additives to enhance the strength of materials. Furthermore the electronic properties of CNTs suffering deformations are different from those of CNTs of no deformations. Although many researches regarding to tensile and compressive deformations of CNTs have been performed in these two decades, researches devoted to the torsional deformations of CNTs are rarely found. Recently, Kato et al. [2] have performed a firstprinciples study of the energetics and electronic properties of chiral CNTs. They have found that CNTs of moderate diameters have the systematic twist-dependent electronic properties according to their chiral indices, whereas CNTs of small diameters have the noticeable but individually different twist dependences. Hence, there still remain some unknown characteristics of twist dependences of CNTs of small diameters. In this paper, the torsional deformations of single-walled carbon nanotubes (SWNTs) of the chiral indices (5,0) and (5,1) are investigated using first-principles calculation. The energies and band gaps of the SWNTs under torsions are obtained. MODELS AND METHOD OF SIMULATION Figures 1 shows the models for the (5,0) SWNT under torsions of the specific angles of twist (a) 0 deg/Å, (b) 1.88 deg/Å, (c) 3.38 deg/Å, and (d) 5.63 deg/Å; the definition of the specific angle of twist θis shown in (e). The structural relaxations and energy minimizations for these
structures are performed. Figures 2(a) and 2(b) show the developed models for the (5,0) and (5,1) SWNTs, respectively, to calculate the band structures of the SWNTs under torsions; in these figures, the angle φis related with the specific angle of twistθand defined byφ=tan-1(rθ), where r is the radius of a SWNT. For all the models, t
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