# A Review of Double-Walled and Triple-Walled Carbon Nanotube Synthesis and Applications
## 1 Introduction and Motivation
### Double- and Triple-Walled Carbon Nanotubes  
DWNTs and TWNTs may be understood as two and three concentric SWNTs, respectively, which interact with each other through interlayer (IL) interactions, which are mediated by weak van der Waals forces. The magnitude of these IL interactions will change according to the chirality combinations between the pairs \((n,m)@(n^{\prime},m^{\prime})\) in a DWNT or among the set \((n,m)@(n^{\prime},m^{\prime})@(n^{\prime\prime},m^{\prime\prime})\) in a TWNT [30; 31; 32; 33; 34; 35; 36; 37; 38]. Namely, [PERSON] _et al_. predicted that the IL interactions would play different roles in the DWNT structure and showed that the stability of the double-walled structure does not strongly depend on the \((n,m)\) pairs of the tubes constituting the DWNT, but the van der Waals-related barrier potential for the relative motion of the inner and outer tubes depends strongly on the  
Figure 2: **(a)** Schematic drawing of an ambipolar semiconducting single-walled carbon nanotube (SWNT) device and (b) infrared emission intensity during repeated sweeps of the drain potential as a function of gate voltage. Reproduced with permission form [12], Copyright The American Association for the Advancement of Science, 2003. **(c)** Schematic of a typical split-gate device for photocurrent generation under focused optical illumination and (d) a spatially-resolved photocurrent two-dimensional map with a continuous laser excitation emitting at the wavelength 532 nm and optical power density 25 W/cm\({}^{2}\) for a device of diameter d = 1.8 nm. Scale bar, 1 mm. Reproduced with permission from [15], Copyright The American Association for the Advancement of Science, 2009. \((n,m)\) pairs [38]. This calculation has been further confirmed by [PERSON] and [PERSON] [37]. These theoretical predictions were proven accurate with the successful experimental demonstration of carbon nanotube-based nano-motors and nano-oscillators, as discussed further in the text, in Section 5. It is worth commenting that these multi-walled systems bring the advantage of mixing semiconducting (S) and metallic species (M), which extends the range of applications of DWNTs and TWNTs [39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52; 53]. Moreover, the effectiveness of this mixing is directly related to the van der Waals forces mediating the interlayer interactions. In other words, for weak IL interactions, the tubes composing the multi-walled systems would behave independently of each other [54; 55; 30; 31; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 51; 52; 5  
Recently, [PERSON] _et al_. [55] observed shifts in the resonance energies of incommensurate DWNT systems, which were related to the IL interactions present in those DWNTs, as shown in Figure 4a,b. This was the first measurement suggesting that Moir\(\acute{e}\) patterns were formed for certain configurations of inner@outer tubes in DWNT systems. These experimental results were explained by [PERSON] _et al_. [54] in their theoretical work, which shows that DWNT systems indeed present Moir\(\acute{e}\) patterns for certain chiral angle combinations between the SWNTs constituting the DWNTs. These DWNTs can be described in terms of supercells, and in these cases, the IL interactions are strong enough to cause changes in the electronic properties of each constituent SWNT within a DWNT system (see Figure 4c). Figure 3: Illustration of the possible flavors or metallicities to be obtained for (**a**) double-walled carbon nanotubes and (**b**) triple-walled carbon nanotubes. (**c**) The Raman spectrum of a \((18,5)\)@\((27,5)\) double-walled carbon nanotube (DWNT) and (**d**) the Raman spectrum of a \((15,13)\)@\((31,4)\) DWNT. Both spectra show a strong blueshift in the radial breathing mode (RBM) frequencies from those SWNTs constituting the DWNTs (shown by the dashed lines). The insets in (**c**) and (**d**) show the Rayleigh spectra for the respective DWNTs. Reproduced with permission from [56], Copyright Nature Publishing Group, 2013. [PERSON] _et al_.