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Single wall carbon nanotubes grown entirely from 13-C form an ideal system tostudy the effect of electron interaction on nuclear magnetism in one dimension.If the electrons are in the metallic, Luttinger liquid regime, we show thateven a very weak hyperfine coupling to the 13-C nuclear spins has a strikingeffect: The system is driven into an ordered phase, which combines electron andnuclear degrees of freedom, and which persists up into the millikelvin range.In this phase the conductance is reduced by a universal factor of 2, allowingfor detection by standard transport experiments.

Nuclear Magnetism and Electronic Order in 13C Nanotubes