The electronic properties of a single-walled carbon nanotube are determined by the chiral indices (n, m), which describe how the graphene sheet is rolled: it is metallic if n − m is a multiple of 3 and semiconducting otherwise. Which of the following is metallic?

Answer: A. The (6, 6) armchair tube

A single-walled carbon nanotube is a cylinder made by rolling a graphene sheet so that the chiral vector Ch = na₁ + ma₂ becomes the circumference. Whether it is metallic or semiconducting depends on whether wave vectors passing through the K point, where the graphene bands touch, are allowed around the circumference, and the condition is that n − m is a multiple of 3. (6, 6) has n − m = 0, so it is metallic, and all armchair tubes, with n = m, are metallic. (10, 0) has n − m = 10 and (7, 5) has n − m = 2; neither is a multiple of 3, so both are semiconducting. Zigzag tubes (m = 0) are metallic only when n is a multiple of 3. For randomly chosen chiral indices, about one third are metallic and two thirds semiconducting.