Superconductivity in One and Two Dimensions. II. Charged Systems

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Abstract
In an earlier paper the Ginzburg-Landau free energy functional was used to calculate the effect of thermodynamic fluctuations on the off-diagonal correlation function and we found no off-diagonal long-range order in one- and two-dimensional systems. It has been pointed out that, for a charged system, the use of the Ginzburg-Landau free energy functional is in error for arbitrary nonequilibrium values of the order parameter since the electrostatic energy of the charge fluctuations associated with an arbitrary order parameter is not included in the free energy functional. We have not succeeded in a direct generalization of the free energy functional so we are forced to proceed by inference from the generalized random phase approximation (RPA). We find that, for uncharged systems, the RPA gives a linearization of the results obtained earlier using the Ginzburg-Landau theory. For charged systems we find in the RPA results similar to those obtained for uncharged systems. From this we conclude that it is very likely that, as in uncharged systems, there will be no ODLRO in charged infinite one- and two-dimensional systems.