Peierls instability in carbon nanotubes: A first-principles study

We present a first-principles study of Peierls distortions in trans-polyacetylene, polyacene, and armchair $\left(n,n\right)$ carbon nanotubes. Our findings suggest that the ground-state geometries of armchair $\left(n,n\right)$ carbon nanotubes, with $n$ up to 6, exhibit a Peierls distortion as it is found for trans-polyactetylene. In contrast to previous studies in which no Peierls distortion is found with conventional local and semilocal density functionals, we use a hybrid functional whose exact-exchange admixture has been specifically optimized for the problem at hand.

Figure 1

Most stable configurations obtained for PAc and $\left(n,n\right)$ CNTs with $x>0$. Here the double, aromatic and single bonds notation is used to emphasize that the bond lengths are ordered as follows $A<B<C$.

Figure 2

(Color online) Dimerization amplitude (top panel) and band gap (bottom panel) as a function of the percentage of exact exchange $\left(x\right)$ included in the functional. The shaded area indicates the range of $x$ yielding the best agreement between calculated and experimental $t\text{-PA}$ bond lengths. The insets zoom in on the small-$x$ region.

Figure 3

Bands structures of (3,3) tube for increasing exact exchange mixing; from left to right $x$ takes the values 0.0, 0.2, and 0.3.