WEAK-LOCALIZATION EFFECTS IN 2-DIMENSIONAL AND ONE-DIMENSIONAL ELECTRON-SYSTEMS ABOVE THE SUPERCONDUCTING TRANSITION

The weak-localization correction to the conductivity in two- and one-dimensional electron systems close to the superconducting transition is studied. We calculate directly the correction to the conductivity and take into account the exact frequency dependence of the phase relaxation time due to the electron-electron interaction in the Cooper channel (superconducting fluctuations). It is shown that in two dimensions the effective phase relaxation time due to the interaction in the Cooper channel close to the superconducting transition has practically the same order of magnitude and the same functional form as the phase relaxation time due to the Coulomb interaction. This result strongly differs from earlier works in which the electron phase relaxation time was calculated separately for zero electron frequency. In the one-dimensional case the phase relaxation due to the interaction in the Cooper channel near the superconducting transition is more important than the relaxation due to the Coulomb interaction.