Twist instability in strongly correlated carbon nanotubes

We show that strong Luttinger correlations of the electron liquid in armchair carbon nanotubes significantly enhance the onset temperature of the putative twist Peierls instability and lead to its 1/R3 dependence on the tube radius. Depending on the values of the coupling constants the umklapp processes can either assist or compete with the twist instability. In the case of a competition the umklapp processes win in wide tubes. In narrow tubes the outcome of the competition depends on the relative strength of the e-e and e-ph backscattering. Our estimates show that the twist instability may be realized in freestanding (5,5) tubes.