Incompatibility of BCS pairing and the Peierls distortion in one-dimensional systems. I. Mean-field theory
- 1 November 1974
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 10 (9), 3821-3831
- https://doi.org/10.1103/physrevb.10.3821
Abstract
The relationship between the BCS superconducting and Peierls insulating phase transitions in one-dimensional systems is investigated within mean-field theory. This calculation lays the essential theoretical groundwork for a treatment of fluctuations in the two order parameters which is presented in a companion paper. The model Hamiltonian used here is equivalent to the reduced BCS Hamiltonian when the Peierls gap vanishes and also equal to the mean-field approximation to the Fröhlich Hamiltonian, in the presence of electron-electron interactions, when the BCS gap is zero. The two coupled gap equations are derived and solved and it is found that the two instabilities are, in general, very incompatible. When the "bare" Peierls transition temperature is greater than the "bare" BCS transition temperature , the system generally orders at and is a Peierls insulator at all lower temperatures. The converse is also true. Only when and are nearly equal will the ordered state be the "mixed" state, that in which both order parameters are simultaneously nonzero. This mixed state is shown to exhibit a "one-dimensional Meissner effect." As a side issue, the effect of electron-electron interactions on the Peierls transition (when the BCS gap is zero) is also investigated; it is shown that electron-electron interaction effects are important. Repulsive interactions lower , while attractive interactions raise . These effects are sufficiently severe so that in jellium, with only Coulombic interactions present, is identically zero.
Keywords
This publication has 11 references indexed in Scilit:
- Incompatibility of BCS pairing and the Peierls distortion in linear chain systemsSolid State Communications, 1974
- Theory of fluctuation superconductivity from electron-phonon interactions in pseudo-one-dimensional systemsPhysical Review B, 1974
- Theory of the peierls soft-mode induced superconducting instability of a linear chain conductorSolid State Communications, 1973
- Conductivity, Superconductivity, and the Peierls InstabilityPhysical Review Letters, 1973
- Fluctuation Effects at a Peierls TransitionPhysical Review Letters, 1973
- Superconducting fluctuations and the peierls instability in an organic solidSolid State Communications, 1973
- Possibility of Synthesizing an Organic SuperconductorPhysical Review B, 1964
- Comparison of two models for the many-fermion systemAnnals of Physics, 1961
- Structure of Nuclear MatterPhysical Review Letters, 1960
- On the theory of superconductivity: the one-dimensional caseProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1954