One- and two-dimensional carbon nanostructures based on unfolded buckyballs: An ab initio investigation of their electronic properties

Motivated by recent experimental research on the temperature-induced unfold of ${\mathrm{C}}_{60}$ molecules, carbon nanostructures are proposed based on the complex assemblies of molecules resulting from the hierarchical unzipping of fullerene cages. Such assemblies can result in either 1D ribbons or 2D porous membrane systems whose electronic structure is studied here using ab initio calculations. These ribbons and membranes show versatile electronic behaviors such as direct or indirect band gaps that can be fine tuned as a function of the details of the atomic structure, such as the type of assembly and ribbon width.

Figure 1

(a)–(e) Illustration of the chemical process producing planar structures [which we call A (d) and B (e) molecules] from initial fullerene (a) structures. (f) Identification of different sites $\alpha$ and $\beta$ to link A and/or B molecules in order to create the complex assemblies studied in this work.

Figure 2

Different 1D and 2D assemblies based on open-fullerene A and B molecules. Ribbons are classified according to the relative orientation of successive molecules: (a) $\mathrm{GNR}-l-\mathrm{AB}$, (b) $\mathrm{GNR}-l-\mathrm{BB}$, (c) $\mathrm{GNR}-t-\mathrm{AB}$, (d) $\mathrm{GNR}-t-\mathrm{BA}$, (e) $\mathrm{GNR}-o-\mathrm{AA}$, and (f) $\mathrm{GNR}-o-\mathrm{AB}$. Two-dimensional structures are named (g) sheet 1, (h) sheet 2, and (i) sheet 3.

Figure 3

(a) Electronic band structure, (b) PDOS contributions, and LDOS for the conduction (c) and valence (d) bands at the $\mathrm{\Gamma }$ point for the $\mathrm{GNR}-l-\mathrm{AB}$ system. The same information for $\mathrm{GNR}-l-\mathrm{BB}$ is shown in (e)–(h).

Figure 4

In (a) and (b) we show the atomic structures for the ZGNR-2 and AGNR-5 systems, respectively. A representation of how the $\mathrm{GNR}-l-\mathrm{AB}$ and $\mathrm{GNR}-l-\mathrm{BB}$ structures can be understood from finite pieces of ZGNRs and AGNRs is shown in (c) and (d), respectively.

Figure 5

(a) Electronic band structure, (b) PDOS contributions, and LDOS for the conduction (c) and valence (d) bands at the $\mathrm{\Gamma }$ point for the $\mathrm{GNR}-t-\mathrm{AB}$ system. The same information for $\mathrm{GNR}-t-\mathrm{BA}$ is shown in (e)–(h).

Figure 6

(a) Electronic band structure, (b) PDOS contributions, and LDOS for the bottom of the conduction band (c) and the top of the valence band (d) for the $\mathrm{GNR}-o-\mathrm{AA}$ system. The same information for $\mathrm{GNR}-o-\mathrm{AB}$ is shown in (e)–(h).

Figure 7

(a) Sheet 1 atomic structure together with its lattice vectors and a plot of the valence and conduction bands over the whole Brillouin zone. (b) Color map plot for the valence (lower) and conduction (upper) bands over the Brillouin zone. (c) Electronic band structure of sheet 1 along high-symmetry lines on the Brillouin zone.

Figure 8

(a) Sheet 2 structure together with its lattice vectors and a plot of the valence and conduction bands over the whole Brillouin zone. (b) Color map plot for the valence (lower) and conduction (upper) bands over the Brillouin zone. (c) Electronic band structure of sheet 2 along high-symmetry lines on the Brillouin zone.

Figure 9

(a) Sheet 3 structure together with its lattice vectors and a plot of the valence and conduction bands over the whole Brillouin zone. (b) Color map plot for the valence (lower) and conduction (upper) bands over the Brillouin zone. (c) Electronic band structure of sheet 3 along high-symmetry lines on the Brillouin zone.

Figure 10

Electronic band gap of the $\mathrm{GNR}-x-\mathrm{YZ}-n$ structures for $n=1,2,\cdots ,10$ and the $n\to \infty$ limit as calculated by tight binding.