Effect of quasiparticles on interlayer transport in highly anisotropic layered superconductors

We have performed a microscopic calculation of the dielectric response function in highly anisotropic layered superconductors and used the developed approach to obtain the frequency-dependent London penetration length and conductivity in the case of d-wave pairing for currents perpendicular to the layers. We consider a BCS model with coherent interlayer tunneling of electrons and take into account contributions from both superconducting electrons and quasiparticles to the dielectric response. We show that quasiparticles change the low-temperature behavior of the penetration length in the intermediate frequency range where the frequency is smaller than the superconducting order parameter but larger than the inverse quasiparticle scattering time. The obtained results are used to describe the low-temperature behavior of the Josephson plasma resonance, in particular the temperature dependence of the resonance frequency and the resonance linewidth in zero external magnetic field. We compare our results with the available experimental data for Tl₂Ba₂CuO₆ and Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) and show that results of a BCS model with coherent interlayer tunneling for the dc c-axis resistivity in the superconducting state are inconsistent with experimental data for underdoped and optimally doped Bi-2212 crystals.