The one-dimensional Wigner crystal in carbon nanotubes

A dilute system of electrons interacting through long-range Coulomb forces has been predicted to form a periodic solid known as a Wigner crystal. To date, this state has been observed directly only in two-dimensional systems. Here, using low-temperature single-electron transport spectroscopy, we show that the hole gas in low-disorder semiconducting carbon nanotubes forms a one-dimensional Wigner crystal. In an axial magnetic field, we observe three distinct regimes of spin and isospin polarization as carrier density is varied. We explain these regimes in terms of a Wigner crystal picture based on a gapped Luttinger liquid model, with the carriers represented by spatially localized solitons. Our observations could enable greater control over the behaviour of the spatially separated system of carriers. Such control, combined with the inherently long coherence times of carriers in carbon nanotubes, could prove useful in the development of solid-state quantum computing.