tailieunhanh - Science Technology Carbon Nanotubes Part 5

Tham khảo tài liệu 'science technology carbon nanotubes part 5', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 70 W EK r 5 which is equivalent to the relativistic Dirac equation 12 . The energy bands are given by n k AI A2 7y2K p n 2 Y2 2 A 2 A22. 6 This shows that the gap given by Eg 2fAi A22 opens up in the absence of a magnetic flux. The gap parameters Al and A2 are determined by the minimisation of the total energy given by 4 ĩ Ẹ4- so KD A ĩế Nfậ-- n - k 2 2 f where is the valence-band energy K and Ki are the force constants for the in- and out-of-plane distortions respectively and N is the total number of carbon atoms. Further and fl are defined by A 1 and A2 2 2- We have introduced a cutoff function go in order to extract the contribution from the states in the vicinity of the top of the valence band. The results are independent of the choice of cutoff functions as long as the function decays smoothly with energy and the cutoff energy is sufficiently large. The gap parameters are determined under the condition that the total energy becomes minimum and it is found that two kinds of distortions cannot coexist and that a distortion having a larger effective coupling constant À V3a 2 rcẪy occurs where K f Ki fi with i 1 or 2. The gap parameter is obtained as EgW gẠẠT A 2. P0 LEg 4ny Eg 2Mexp - 1 - c c . 8 The gap parameter or lattice distortion vanishes in the critical AB flux which opens the gap as large as that due to the distortion. For 0 the gap decreases exponentially as a function of the circumference L a. Table 2 gives some examples for an in-plane Kekulé distortion. For out-of-plane distortion the coefficient fl - A2 m2 is expected to be proportional to a L since fl becomes nonzero for the finite curvature. Thus the coupling constant is proportional to ứ L 2 and the gap decreases very rapidly with the diameter as exp - L a 3 It is concluded that metallic CNTs are quite 71 stable against lattice distortions and hold metallic properties even at low temperatures except in exfremely narrow CNTs. The situation changes drastically in the presence of a high .

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