Effective action approach and Carlson-Goldman mode in d-wave superconductors

We theoretically investigate the Carlson-Goldman (CG) mode in two-dimensional clean d-wave superconductors using the effective ``phase only'' action formalism. In conventional s-wave superconductors, it is known that the CG mode is observed as a peak in the structure factor of the pair susceptibility $S(\Omega, \mathbf{K})$ only just below the transition temperature T_c and only in dirty systems. On the other hand, our analytical results support the statement by Y.Ohashi and S.Takada, Phys.Rev.B {\bf 62}, 5971 (2000) that in d-wave superconductors the CG mode can exist in clean systems down to the much lower temperatures, $T \approx 0.1 T_c$. We also consider the manifestations of the CG mode in the density-density and current-current correlators and discuss the gauge independence of the obtained results.Comment: 23 pages, RevTeX4, 12 EPS figures; final version to appear in PR

Nonequilibrium relaxation in neutral BCS superconductors: Ginzburg-Landau approach with Landau damping in real time

We present a field-theoretical method to obtain consistently the equations of motion for small amplitude fluctuations of the order parameter directly in real time for a homogeneous, neutral BCS superconductor. This method allows to study the nonequilibrium relaxation of the order parameter as an initial value problem. We obtain the Ward identities and the effective actions for small phase the amplitude fluctuations to one-loop order. Focusing on the long-wavelength, low-frequency limit near the critical point, we obtain the time-dependent Ginzburg-Landau effective action to one-loop order, which is nonlocal as a consequence of Landau damping. The nonequilibrium relaxation of the phase and amplitude fluctuations is studied directly in real time. The long-wavelength phase fluctuation (Bogoliubov-Anderson-Goldstone mode) is overdamped by Landau damping and the relaxation time scale diverges at the critical point, revealing critical slowing down.Comment: 31 pages 14 figs, revised version, to appear in Phys. Rev.

Effects of spin-flip scattering on the dynamics of the superconducting order parameter

Measurements of the imaginary part of the pair-field susceptibility X'' have been carried out on dirty-limit Al-Er alloy films. Aluminum films with erbium concentrations of up to one atomic percent were incorporated as the low T/sub c/ film of an asymmetric Josephson junction. The excess current I/sub ex/ due to pair tunneling was measured as a function of the bias voltage V and of the magnetic field H, applied in the plane of the junction, at temperatures within 20% of the critical temperature T/sub c/. Comparison to theory was facilitated by noting that X''(..omega..,k) varies as I/sub ex/(V,H) where the frequency ..omega.. and wave-number k are related to V and H via the Josephson relations