CDW/Normal metal/CDW junctions and nanoconstrictions in crystals of the quasi-one-dimensional conductor NbSe$_3$ are manufactured using a focused-ion-beam. It is found that the low-temperature conduction of these structures changes dramatically and loses the features of the charge-density-wave transition. Instead, a dielectric phase is developed. Up to 6-order power-law variations of the conduction as a function of both temperature and electric field can be observed for this new phase. The transition from quasi-one-dimensional behavior to one-dimensional behavior is associated with destruction of the three-dimensional order of the charge-density waves by fluctuations. It results in a recovery of the Luttinger-liquid properties of metallic chains, like it takes place in sliding Luttinger liquid phase.
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