  Electron-electron interactions strongly affect the behavior of
low-dimensional systems. In one dimension (1D), arbitrarily weak interactions
qualitatively alter the ground state producing a Luttinger liquid (LL) which
has now been observed in a number of experimental systems. Interactions are
even more important at low carrier density, and in the limit when the
long-ranged Coulomb potential is the dominant energy scale, the electron liquid
is expected to become a periodically ordered solid known as the Wigner crystal.
In 1D, the Wigner crystal has been predicted to exhibit novel spin and magnetic
properties not present in an ordinary LL. However, despite recent progress in
coupled quantum wires, unambiguous experimental demonstration of this state has
not been possible due to the role of disorder. Here, we demonstrate using
low-temperature single-electron transport spectroscopy that a hole gas in
low-disorder carbon nanotubes with a band gap is a realization of the 1D Wigner
crystal. Our observation can lead to unprecedented control over the behavior of
the spatially separated system of carriers, and could be used to realize solid
state quantum computing with long coherence times.
