Incompatibility of BCS pairing and the Peierls distortion in one-dimensional systems. II. Fluctuation effects

Abstract

The relationship between the BCS superconducting and the Peierls insulating phase transitions in one-dimensional systems is investigated. This is the second in a series of two papers and treats the effects of simultaneous fluctuations in both order parameters. The coefficients appearing in the Landau-Ginsburg free-energy functional are calculated from the mean-field theory results of the first paper (I) and the statistical-mechanical properties are obtained by expressing the partition function as a functional integral over the Landau-Ginsburg free-energy functional. The problem is reduced to solving for the eigenfunctions and eigenvalues of a particular two-dimensional anharmonic oscillator. Results for the fluctuations and correlation lengths of both order parameters are presented both for a narrow-critical-region model, closely related to that examined by Scalapino, Sears, and Ferrell for the case of one order parameter, and for a wide-critical-region model, based on the approach of Lee, Rice, and Anderson (LRA), who also considered only a single order parameter. The conclusions reached in both models are that fluctuations associated with the lower-critical-temperature order parameter are strongly suppressed. In addition, the correlation length of this order parameter does not appear to grow large as the temperature is lowered. These results support those obtained in I: The BCS and Peierls phase transitions are generally incompatible. Several unexpected and possibly unphysical features of the LRA model for one order parameter are also discussed.