Usually, in optical spectra of double-walled carbon nanotubes (DWCNTs), weak van der Waals coupling between the layers leads only to a small shift of transition energies with respect to their values in pristine single-walled nanotubes. However, recent results have shown that the Rayleigh spectrum of the DWCNT (12,11)@(17,16) contains additional peaks. Using the tight-binding approximation, we demonstrate that in specific DWCNTs the interlayer coupling can slightly modify the band structure of pristine nanotubes in such a way that the unconventional inter-tube electronic transitions become possible and additional peaks in the DWCNT optical spectrum appear. Using the known experimental data on 118 optical transitions in DWCNTs, in addition to the recently published case, we reveal six more DWCNTs with inter-tube transitions and obtain geometrical selection rules permitting them. In a few dozen of DWCNTs our approach yields the energies of electronic transitions close to the experimentally observed ones and may be useful for structural identification of this type of nanotubes.

中文翻译：

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双壁碳纳米管的能带结构和管间光学跃迁

通常，在双壁碳纳米管（DWCNT）的光谱中，各层之间的弱范德华耦合仅导致跃迁能量相对于原始单壁纳米管的值发生很小的偏移。但是，最近的结果表明，DWCNT（12,11）@（17,16）的瑞利光谱包含其他峰。使用紧密结合的近似值，我们证明了在特定的DWCNT中，层间耦合可以稍微改变原始纳米管的能带结构，从而使非常规的管间电子跃迁成为可能，并且在DWCNT光谱中出现其他峰。除了最近发表的案例之外，使用DWCNT中118个光学跃迁的已知实验数据，我们揭示了另外六个具有管间过渡的DWCNT，并获得允许它们的几何选择规则。在几十种DWCNT中，我们的方法产生的电子跃迁能量接近实验观察到的能量，可用于此类纳米管的结构鉴定。