Single-walled carbon nanotube bundle under hydrostatic pressure studied by first-principles calculations

The structural, electronic, optical, and vibrational properties of the collapsed (10,10) single-walled carbon nanotube bundle under hydrostatic pressure have been studied by first-principles calculations. Some features are observed in the present study: First, a collapsed structure is found, which is distinct from both of the herringbone and parallel structures obtained previously. Second, a pseudogap induced by the collapse appears along the symmetry axis $\Gamma X$. Third, the relative orientation between the collapsed tubes has an important effect on their electronic, optical, and vibrational properties, which provides an efficient experimental method to distinguish unambiguously three different collapsed structures.

Figure 1

(a) Loading curve for (10,10) SWNT bundle as a function of hydrostatic pressure. Snapshots of the cross section of a (10,10) SWNT bundle at $3\mathrm{GPa}$: (b) the parallel structure, (c) the in-between structure, and (d) the herringbone structure.

Figure 2

(Color online) The calculated electronic band structures along the nanotube symmetry axis $\Gamma X$ of (a) an individual (10,10) SWNT at $0\mathrm{GPa}$, (b) a (10,10) SWNT bundle at $0\mathrm{GPa}$, and of three collapsed structures at $3\mathrm{GPa}$: (c) the parallel structure, (d) the in-between structure, and (e) the herringbone structure. Inset of (e) shows the pseudogap at the Fermi level in an energy region of $-0.15–0.15\mathrm{eV}$. The Fermi level is set at zero.

Figure 3

The calculated density of states for three collapsed structures at $3\mathrm{GPa}$: (a) the parallel structure, (b) the in-between structure, and (c) the herringbone structure. The Fermi level is set at zero.

Figure 4

(Color online) The calculated imaginary part (absorptive part) of dielectric function polarized along $X$, $Y$, and $Z$ directions, respectively, for (a) an individual (10,10) SWNT at $0\mathrm{GPa}$, (b) a (10,10) SWNT bundle at $0\mathrm{GPa}$, and for three collapsed structures at $3\mathrm{GPa}$: (c) the parallel structure, (d) the in-between structure, and (e) the herringbone structure.

Figure 5

(Color online) The calculated nonresonant Raman spectra of (a) a (10,10) SWNT bundle at $0\mathrm{GPa}$ [its inset shows that of an individual (10,10) SWNT], and of three collapsed structures at $3\mathrm{GPa}$: (b) the parallel structure, (c) the in-between structure, and (d) the herringbone structure.

Figure 6

(Color online) The eigenfrequencies and eigenvectors of some raman-active vibration modes for the different collapsed structures at $3\mathrm{Gpa}$: (a) the parallel structure, (b) the in-between structure, and (c) the herringbone structure. The small circles represent the carbon atoms and the straight lines between them indicate the bonds. The arrows represent the atomic motions. Deeper color arrow means the corresponding atom is nearer to the reader.