Penetration depth anisotropy due to the proximity effect in ad-density-wave scenario

Abstract

We calculate the penetration depth $\ensuremath{\lambda}$ along the $a$ and $b$ directions in the presence of the pseudogap and superconducting phases for a simple model that incorporates two layers---a $\mathrm{Cu}{\mathrm{O}}_{2}$ plane and a CuO chain per unit cell. The CuO chains become superconducting due to the proximity to the planes below the critical temperature. The pseudogap phase has been considered to be a result of the $d$-density-wave (DDW) phase. The temperature dependence of ${\ensuremath{\lambda}}_{a}$ is always different from ${\ensuremath{\lambda}}_{b}$ as it depends on the induced gap in the chains. The DDW phase plays a vital role not only to distinguish the temperature dependence of ${\ensuremath{\lambda}}_{b}$ from that of ${\ensuremath{\lambda}}_{a}$ but also to identify the mixed phase from the pure phase of these superconductors.