Theory of Basov correlation between penetration depth and conductivity along the c-axis in high-T_c cuprate superconductors

We present a theoretical explanation for the correlation between the c-axis penetration depth and the c-axis conductivity (σ_c) in high-T_c cuprates which was experimentally discovered by Basov et al. [Phys. Rev. B 50 (1994) 3511]. Our model is based on the BCS theory for the quasi-two-dimensional d-wave superconductivity in which the strength of the incoherency in the c-axis charge dynamics is controlled by potential scatterings. We show that the Basov correlation is realized when the difference in the magnitude of σ_c among various high-Tc cuprate materials is dominated not by the damping of electrons but by the carrier density and/or the band mass along the c-axis. It is also shown that there exists a correlation between the c-axis Josephson plasma frequency and σ_c in high-T_c cuprates.