One-Dimensional Moiré Superlattices and Flat Bands in Collapsed Chiral Carbon Nanotubes

Abstract

We demonstrate that one-dimensional moirépatterns, analogous to those found in twisted bilayer graphene, can arise in collapsed chiral carbon nanotubes. Resorting to a combination of approaches, namely, molecular dynamics to obtain the relaxed geometries and tight-binding calculations validated against ab initio modeling, we find that magic angle physics occur in collapsed carbon nanotubes. Velocity reduction, flat bands, and localization in AA regions with diminishing moiréangle are revealed, showing a magic angle close to 1°. From the spatial extension of the AA regions and the width of the flat bands, we estimate that many-body interactions in these systems are stronger than in twisted bilayer graphene. Chiral collapsed carbon nanotubes stand out as promising candidates to explore many-body effects and superconductivity in low dimensions, emerging as the one-dimensional analogues of twisted bilayer graphene.

Tuning Magnetic Order in CrI3 Bilayers via Moiré Patterns

“…Similar characteristics have been found in moiré systems for low angles such as graphene, [40] dichalcogenide systems, [35,41] few-layer graphite, [42] carbon nanotubes, [43] among others. New studies on the electronic structure of Bravais-moiré systems varying the angle 𝜃 between 0 • and 360 • are necessary to have a clear trend regarding the electronic and magnetic tuning behavior.…”

Interlayer Interactions in 1D Van der Waals Moiré Superlattices

“…Several theoretical reports quickly followed the above observation of 1D moiré superlattice effect. [140][141][142][143][144] One study predicted strong inter-tube optical transitions in DWNT moiré superlattices when satisfying certain structure requirements. [140] It claimed that the interlayer electronic coupling can modify the band structure in quite a few DWNTs and shift the VHS positions of each constituent SWNTs (Figure 6a), making the inter-tube transitions optically bright and dominate over the intra-tube transitions (indicated by the arrows in the right panel of Figure 6a).…”

“…d) Reproduced with permission. [ 144 ] Copyright 2020, American Chemical Society. e) Reproduced with permission.…”

“…Very interestingly, like the MATBG, similar magic‐angles to have flat moiré bands and vanishing Fermi velocities were recently predicted in another 1D moiré system, flattened carbon nanotubes (FNTs) (Figure 6d). [ 144 ] This hypothesized structure is transformed from a collapsed large‐diameter nearly‐zigzag SWNT (structure model shown in the upper left inset of Figure 6d). Notably, FNTs that are collapsed from nearly‐zigzag nanotubes can even have narrower bandwidths (≈1 meV) than MATBG does (inset on the bottom right of Figure 6d), which potentially makes it a stronger correlated electronic system.…”

“…Copyright 2015, American Physical Society. d) Reproduced with permission [144]. Copyright 2020, American Chemical Society.…”