  We study the influence of non magnetic impurities on the phase diagram of
doped two-leg Hubbard Cu-O ladders. In the absence of impurities this system
posseses d-wave superconducting states and orbital current states depending on
the doping. A single, strong, scatterer modifies its environment locally and
this effect is assessed using a renormalization group analysis. At high doping,
disorder causes intraband instabilities and at low doping it promotes interband
instabilities. In the former case, we extend the boundary conformal field
theory method, developed in the context of single chains, to handle the ladder
problem, and we find exact closed-form analytical expressions for the
correlation functions. This allows us to compute experimentally measurable
local quantities such as the nuclear magnetic resonance line broadenings and
scanning tunnelling microscope profiles. We also discuss the low doping regime
where Kondo physics is at play, making qualitative predictions about its
nature. Insight into collective effects is also given in the many weak
impurities case, based on an RG approach. In this regime, one sees the
interplay between interactions and disorder. We emphasize the influence of the
O atoms on disorder effects both for the single- and for the many-defect
situations.
