Long-range order in quasi-one-dimensional conductors

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We study formation of the charge-density wave long-range order in a system of repulsive 1D electrons coupled to 3D phonons. We show that the CDW can be stabilized by interaction with phonons in quasi-1D crystals and semiconducting nanowires. In the case of metallic atomic chains, interaction with phonons of 3D substrate is not enough, and violation of the translational invariance by commensurable perturbation or disorder is needed. The possibility of stabilization of superconductivity in 1D electrons with attraction by means of tunnel coupling to a 3D metal is considered.