Page 122 - Principles and Applications of NanoMEMS Physics

110 Chapter 3

K’ K’
M’
M’
K K
Γ Γ

k y k y
k x k x
(a)
K’ K’
M M

Γ Γ K K
k k x x

k k y y
(b)

Figure 3-16 (a) A 1D band structure lies at each of the discrete values of k for a (5, 5)
x
armchair CNT, dictated by the circumferential quantization in this direction. The armchair
CNT is metallic. (b) A 1D band structure lies at each of the discrete values of k for a (9, 0)
y
zigzag CNT, dictated by the circumferential quantization in this direction. The zigzag CNT is
semiconducting. (After [46].)
It may be surmised from the slice passing through the K’, K points, see Fig.
3.17, that each channel is four-fold degenerate, on account of spin
degeneracy and the sublattice degeneracy of electrons in graphene [144].

E( k ) )
E( k

K’
K’ K K
k k
E E F F

Figure 3-17. Energy band diagram of metallic CNT for slice through Fermi points K’, K.