Double-walled carbon nanotubes as one-dimensional moir\'{e} crystals

Being multi-shell structure, the well-defined atomic periodicity is hardly realizable in double-walled nanotubes because the periodic units of individual tubes therein cannot match well except very few cases, posing a challenge to understand its physical properties. Here we show that moir\'{e} patterns generated by superimposing atomic lattices of individual tubes are decisive in determining its electronic structures [1]. By using double-walled carbon nanotubes as an example, we demonstrate that even the combination of semiconducting nanotubes with almost the same physical properties such as diameter and energy gap can end up with very different double-walled nanotubes, of which electronic properties vary from metallic to semiconducting and further to insulating states, depending on the interlayer moir\'{e} interference. Our study puts forth a new classification of nanotubes as the first example of one-dimensional moir\'{e} crystals and paves a firm ground to utilize superb technological merits of double-walled carbon nanotubes. [1] Mikito Koshino, Pilkyung Moon, and Young-Woo Son, arXiv:1410.7544 (2014).