a) Write down the equation for the graphene band structure. b) Draw the contour plot for graphene, and label the K, M and K' points. c) On the graphene lattice structure shown below, mark, (4,3) nanotube. d) d) For the (4,3) nanotube, draw the directions of ,, and for a OB a1 a2 OA and kparallel kperpendicular e) For the (4,3) nanotube, draw the allowed lines (sometimes called "cut-lines") in the k- space relative to the contour plot of graphene. f) Calculate the spacing between the allowed lines for the (4,3) nanotube. g) For the (4,3) nanotube, do any of the lines intersect with any of the 6 K points? Is the nanotube metallic or semiconductive.