Energies of Optical Transitions
in Metal and Semiconductor Nanotubes

P. N. D’yachkov

Kurnakov Institute of General and Inorganic Chemistry, Russian Academy of Sciences,
Leninskii pr. 31, Moscow, 119991 Russia

Received January 25, 2005

Abstract—The energies of low-energy optical transitions were calculated, using the linearized attached cylin-
drical waves (LACW) method, as a function of inverse diameter d¹ for (n, n) metal nanotubes with n ranging
from 3 to 12 and for (n, 0) semiconductor nanotubes with n ranging from 10 to 25. The calculations show that
E₁₁ in the metal nanotubes is higher than in the semiconductor nanotubes. Significant violations of the E₁₁ ~
d¹ relationship are observed. For metal nanotubes, the situation is more complex because of the close energies
of the *- and * vertical transitions and because of the intersection of these characteristics in the range
of 0.7 nm^–1 < d¹ < 1.0 nm^–1 (n = 8, 9, 10). For the semiconductor nanotubes, the E₁₁ versus d¹ relationship is
not linear, rather, it is oscillating; the E₁₁(d¹) function alternates between two curves that refer to the (n, 0) nan-
otubes for which division of n by 3 gives 1 or 2 in the residue. On one hand, these features hamper the use of
optical measurements in structure determination for the nanotubes; on the other, new criteria for nanotube clas-
sification appear.

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