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初入门菜鸟拿着这题完全没思路，求大神们指个方向，跪谢!
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In figure 1 a and b below you see a graphene sheets. The chiral vector Ch is drawn to represent a single-walled carbon nanotube with certain chiralities. For both type of tubes you should; a)Determine the chirality of the tube (n, m). b)Calculate the translational vector Th (direction is given by a dotted line) c)Calculate the diameter, and the number of carbon atoms in the unit cell. d)Determine if the tube in figure 1, and 2 are metallic or semiconducting. e)Use the Kataura plot (give reference in your answer where and how you have gathered the information) to derive the energy between the first pair of Van Hove singularities. Give an example of a laser with appropriate wavelength that you would use in a Raman spectroscopy measurement. f)Assume isolated tubes on a substrate with negligible interactions to the substrate, at which wavenumber would you expect to measure its radial breathing mode by Raman spectroscopy. What energy in electron volt does this vibrational energy correspond to? g)If you would calculate the band gaps of carbon nanotubes (or for other semiconductors) by density functional theory, and by considering that this is a ground state approach, why do you think that the band gaps normally are underestimated? Figure 1 a and b. Graphene sheets, with chiral vector, Ch representing a certain type of SWNT-tube. The graphite lattice vectors are shown as red small arrows (a1, and a2), and the direction of the translational vector Th is indicated by a red dotted line.  图片1.png  图片2.png |
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