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We discuss a new mechanism of microwave absorption in s- and d-wave superconductors, which arises in the presence of a dc supercurrent in the system. It produces a contribution to the ac conductivity that is proportional to the inelastic quasiparticle relaxation time. This contribution also determines the supercurrent dependence of the conductivity. It may significantly exceed the conventional contribution because in typical superconductors the inelastic relaxation time is several orders of magnitude longer than the elastic one. We show that the aforementioned contribution to the conductivity may be expressed in terms of the single particle density of states in superconductors in the presence of a dc supercurrent. Our results may enable determination of the inelastic relaxation time in superconductors from microwave absorption measurements.
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We discuss a mechanism of microwave absorption in conventional superconductors which is similar to the Debye absorption mechanism in molecular gases. The contribution of this mechanism to the emph{ac} conductivity is proportional to the inelastic quasiparticle relaxation time $tau_mathrm{mathrm{in}}$ rather than the elastic one $tau_{mathrm{el}}$ and therefore it can be much larger than the conventional one. The Debye contribution to the linear conductivity arises only in the presence of a emph{dc} supercurrent in the system and its magnitude depends strongly on the orientation of the microwave field relative to the supercurrent. The Debye contribution to the nonlinear conductivity exists even in the absence of emph{dc} supercurrent. Since it is proportional to $tau_{mathrm{in}}$ the nonlinear threshold is anomalously low. Microwave absorption measurements may provide direct information about $tau_mathrm{in}$ in superconductors.
Enhanced microwave absorption, larger than that in the normal state, is observed in fine grains of type-II superconductors (MgB$_2$ and K$_3$C$_{60}$) for magnetic fields as small as a few $%$ of the upper critical field. The effect is predicted by the theory of vortex motion in type-II superconductors, however its direct observation has been elusive due to skin-depth limitations; conventional microwave absorption studies employ larger samples where the microwave magnetic field exclusion significantly lowers the absorption. We show that the enhancement is observable in grains smaller than the penetration depth. A quantitative analysis on K$_3$C$_{60}$ in the framework of the Coffey--Clem (CC) theory explains well the temperature dependence of the microwave absorption and also allows to determine the vortex pinning force constant.
We investigate the influence of extended scatterers on the finite temperature and finite frequency microwave conductivity of d-wave superconductors. For this purpose we generalize a previous treatment by Durst and Lee, which is based on a nodal approximation of the quasiparticle excitations and scattering processes, and apply it to the analysis of experimental spectra of YBCO-123 and BSCCO-2212. For YBCO, we find that accounting for a slight spatial extension of the strong scattering in-plane defects improves the fit of the low temperature microwave conductivity to experiment. With respect to BSCCO we conclude that it is necessary to include a large concentration of weak-to-intermediate strength extended scatterers, which we attribute to the out-of plane disorder introduced by doping. These findings for BSCCO are consistent with similar analyses of the normal state ARPES spectra and of STM spectra in the superconducting state, where an enhanced forward scattering has been inferred as well.
We study suppression of superconductivity by disorder in d-wave superconductors, and predict the existence of (at least) two sequential low temperature transitions as a function of increasing disorder: a d -wave to -wave, and then an s-wave to metal transition. This is a universal property of the system which is independent of the sign of the interaction constant in the s-channel
The concept of broken symmetry, that the symmetry of the vacuum may be lower than the Hamiltonian of a quantum theory, plays an important role in modern physics. A manifestation of this phenomena is the Higgs boson in particle physics whose long awaited discovery is imminent. An equivalent mode in superconductors is implicit in the early theories of their collective fluctuations. Spurred by some mysterious experimental results, the theory of the oscillation of the amplitude of superconductivity order parameter, which is the equivalent to the Higgs modes in s-wave superconductors and its identification in the experiments, was explicitly provided. It was also shown that a necessary condition for this to occur is the emergent Lorentz invariance in the superconducting state while the metallic state and the region just below $T_c$ is manifestly non-Lorentz invariant. Here we show that d-wave superconductors, such as the high temperature Cuprate superconductors, should have a rich assortment of Higgs bosons, each in a different irreducible representation of the point-group symmetries of the lattice. We also show that these modes have a characteristic singular spectral structure which can be discovered in Raman scattering experiments.
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