Semiconducting nanotubes derived from a rectangular graphyne: a DFT study

TL;DR

This work investigates semiconducting nanotubes derived from rectangular γ-graphyne (rγGY) by folding the 2D sheet into 1D tubes along armchair and zigzag directions. Using density functional theory (DFT) and zone-folding (ZF) analyses, it links 2D frontier-band character to 1D electronic structure, quantifying curvature-induced band-gap modulation and lattice-direction effects. The results show curvature energy $E_C$ decreases with diameter, and band gaps exhibit even–odd oscillations with chirality and diameter; spin-polarized ground states arise in select narrow tubes. Overall, rγGY nanotubes are robust semiconductors across chiralities, offering tunable electronic properties for nanoscale electronics and sensing.

Abstract

Proposing new ways to organize carbon in 2D nanomaterials has been a relevant strategy in the search for systems with targeted properties for different applications. One focus is the study of fully sp$^2$ non-graphitic networks, with successfully synthesized examples. Hybrid sp-sp$^2$ systems of the graphyne family are a related approach, and many systems have the honeycomb lattice as a base model. However, other examples have been inspired by other lattices as the recently proposed r$γ$GY sheet, which features a semiconducting behavior with highly localized \emph{quasi}-1D states. Here, we investigate how to tune r$γ$GY properties by folding this sheet into nanotube forms. We elucidate mechanisms that determine their electronic structure by means of density functional theory calculations, as well as we identify the interplay involving chirality, diameter, and the emergence of dispersive/localized frontier states on gap modulation through simple extrapolated methods.

Figures (9)

• Figure 1: (a) Atomic structure of the r$\gamma$GY sheet, with its lattice vectors $\mathbf{a}_1$ and $\mathbf{a}_2$ represented by the blue arrows. Here, the projections of the unit cells of the (3,0) and (0,4) tubes over the r$\gamma$GY sheet are represented by the dashed purple and blue rectangles, while their $\mathbf{C}_h$ ($\mathbf{T}$) vectors are represented by red (green arrows). (b) Example of a $(n,0)$ nanotube with $n=4$. (c) Example of a $(0,m)$ nanotube with $m=4$.
• Figure 2: Curvature energy as a function of diameter for $(n,0)$ and $(0,m)$ r$\gamma$GYTs.
• Figure 3: (a) Electronic structure of r$\gamma$GY represented over high-symmetry lines of the BZ. The yellow (cyan) shaded areas represent the $k$-space paths parallel to the $\mathbf{b}_1$ ($\mathbf{b}_2$) vector of the reciprocal lattice. E1-E6 represent important energy levels from the frontier bands. (b) Density of states of r$\gamma$GY. (c) Real part of the wavefunction for the E1-E6 energy levels indicated in (a), with cyan and yellow clouds representing portions of the wavefunction with opposite sign. (d) Valence and conduction bands of r$\gamma$GY are represented by a surface plot over the entire BZ, with the Fermi energy represented by the blue rectangle. (e) Cutting lines for the (4,0) and (0,4) tubes represented over the 2D BZ and over the frontier bands of r$\gamma$GY. (f) Same as (e), but for the (3,0) and (0,3) tubes.
• Figure 4: (a) Electronic band structures of the $(n,0)$ nanotubes, with $n$ from 2 to 12, according to the zone-folding approach. The dashed red lines at $E=0$ indicate the Fermi level. (b) Same as (a), but for the $(0,m)$ nanotubes, with $m$ from 2 to 12. (c) Insets of the frontier states of the valence and conduction bands of the $(2,0)$ tube, with the gap energy region highlighted in green.
• Figure 5: (a) Electronic band structures of the $(n,0)$ nanotubes, with $n$ from 2 to 12, according to explicit DFT calculations (including a previous geometry optimization). The dashed red lines at $E=0$ indicate the Fermi level. (b) Same as (a), but for the $(0,m)$ nanotubes, with $m$ from 2 to 12.