Fig. 2. Zigzag tube.
(a)- (e) are initial structure for zigzag tubes of (n,0) with n=4,5,6,7 and 8, respectively.
(f)- (j) are final structure for zigzag tubes of (n,0) with n=4,5,6,7 and 8, respectively.


Fig. 3. Armchair tube.
(a)-( c) are initial structure for armchair tubes of (n,n) with n=4,5 and 6, respectively.
(d)- (f) are final structure for armchair tubes of (n,n) with n=4,5 and 6, respectively.

Fig. 5. Strain energy as a function of the tube diameter for zigzag and armchair tubes.
Circular tubes obey $\D^\2$ decay. But Buckled tubes do not.

Fig. 7. Band structure and density of states of ziazag tube (6.0).
(a),(b) are for circular tube and ( c),(d) are for buckled tube
Fig. 8. Band structure and density of states of armchair tube (6.6).
(a),(b) are for circular tube and ( c),(d) are for buckled tube

Fig. 9. Young’s modulus as a function of tube diameter for zigzag and armchair tubes.
Circular structures and buckled structures are compared.