Figure 2
Several typical graphs in the parameter space for the graphene tubes with N = 3, 4 and 5.
The graphs are N circles with unit radius. The flux determines the positions of the circle centers. The red and green circles indicate the positions of the origin. The corresponding winding numbers are [N/3] or [N/3] + 1, when the origin circles are red or green. (a1–4), (b1–4) and (c1–4) are obtained by the first equivalent Hamiltonian in Eq. (1), while (a5), (b5) and (c5) by the second equivalent Hamiltonian in Eq. (18). The cross in (a2) indicates two superposed circles.
