Physics – Condensed Matter – Superconductivity
Scientific paper
1999-05-02
Physics
Condensed Matter
Superconductivity
25 pages, 5 figures, references added, Introduction rewritten
Scientific paper
10.1103/PhysRevB.62.6638
We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) $ \theta $ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent non-linear Schr\"{o}dinger Lagrangian (TDNLSL) which preserves the Galilean invariance of the zero temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms which are non-local and which destroy the Galilean invariance. We show that the retarded $\theta$-propagator (in momentum space) can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted temperature, frequency and momentum dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component.
Aitchison Ian J. R.
Lee Dominic J.
Metikas Georgios
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