Magnetic penetration depth and condensate density of cuprate high-Tcsuperconductors determined by muon-spin-rotation experiments

We summarize our results of transverse-field muon-spin-relaxation (TF-μSR) experiments on a variety of polycrystalline cuprate high-${\mathit{T}}_{\mathit{c}}$ superconducting systems. In this paper we present the conditions under which the μSR depolarization rate at low temperatures ${\mathrm{\sigma }}_0$∝${\lambda }_{\mathit{a}\mathit{b}}^{\mathrm{-}2}$(0)∝${\mathit{n}}_{\mathit{s}}$(0)/${\mathit{m}}_{\mathit{a}\mathit{b}}^{\mathrm{*}}$ is determined in a unique way by the doping state of ${\mathrm{CuO}}_2$ planes and the consequent critical temperature ${\mathit{T}}_{\mathit{c}}$. Disorder and pinning effects due to various sorts and amounts of dopant atoms do not affect ${\mathrm{\sigma }}_0$. From our results on ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$, ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_4$ ${\mathrm{O}}_8$, and ${\mathrm{Y}}_2$ ${\mathrm{Ba}}_4$ ${\mathrm{Cu}}_7$ ${\mathrm{O}}_{15\mathrm{-}\mathrm{\delta }}$ (systems having both planes and chains) we conclude that a superconducting condensate is not only formed in the ${\mathrm{CuO}}_2$ planes but is induced additionally in the CuO chains. This chain condensate is rapidly suppressed by any disorder in the chains and depends strongly on the oxygen ordering.