The role of Coulomb screening in quasi one-dimensional conductors

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Abstract
The electrons of the system of conducting linear chains with lattice parameters d∥ and d⊥ are assumed to interact through the long-range Coulomb forces. Assuming further that the ratio ν of the first-neighbour Coulomb interaction e2/d∥ to the band-width is small, the problem is treated in the parquet approximation. The parquet diagrams are evaluated using the non-logarithmically screened Coulomb interaction for the forward scattering and the bare Coulomb interaction for the backward scattering. The weak interchain backward scattering is neglected. The parquet approximation eliminates then the screened interchain forward scattering. The three-dimensionality enters the results through the screening of the on-chain forward interaction. This screening is inefficient in the loosely packed chains d⊥ >> d∥. The 2 KF-CDW correlation function of the corresponding Tomonaga model shows then a power law singularity with a power which itself is logarithmically singular. In the closely packed chains the important screening is dynamic. It is very efficient and the usual power laws are recovered. The Coulomb contribution to g2 is however logarithmically enhanced with respect to the first-neighbour interaction ν, i.e. it is equal to ν log d2⊥/νd2∥ . The long-range forces thus enhance the tendency to the formation of the 2 kF-CDW or SDW. In the closely packed chains the effect is weakest and with the help of phonons the superconducting regime can be attained