Current instability and diamagnetism in small-diameter carbon nanotubes

We investigate the electronic instabilities in carbon nanotubes of short radius, looking at the scaling behavior of the different correlations and charge stiffnesses at low energies. We show that the Luttinger liquid behavior breaks down in the undoped (3,3) nanotubes at low temperatures, due to the appearance of soft modes in the sector of current excitations. The phenomenology derived from this regime is consistent with the development of a gap in the single-particle spectrum as well as with a divergent diamagnetic susceptibility, as observed in the experiments carried out in carbon nanotubes of small diameter.

Figure 1

(Color online) Phase diagram of (3,3) (top) and (5,0) (bottom) CN in terms of the Coulomb potential $V$ (in units of $v_F$) and the effective coupling of the phonon-exchange interaction $G=4\mid g\mid ∕\pi v_F$. The thick lines are boundaries between the different phases characterized by the breaking of the parameters $K_{\pm }$ and $K_0$ at low temperature scales. In the (3,3) nanotubes, CDW correlations at zero momentum are dominant at the singular point, but with low strength represented by the contours of constant CDW response function $R=2,4,8,16,32,64$ (from top to bottom). For the (5,0) nanotubes, three different regimes arise with strong correlations at the singular point of $K_{-}$ or $K_0$, given by the dominance of the $2k_F$ CDW (white area), the $2k_F$ spin-density wave (light area), or the $s$-wave SC response function (dark area).

Figure 2

Plot of the density of states $n$ as a function of the energy $\epsilon$ (in units of $E_c$) for $V=0.75\pi v_F$ and $4\mid g\mid ∕\pi v_F=0.2$. The curves correspond to values of minus the logarithm of the temperature scale $l=3.21$, 3.225, 3.232, 3.235, and 3.236.