Effect of proximity coupling of chains and planes on the penetration-depth anisotropy in YBa2Cu3O7

We calculate the penetration depth λ in the a, b, and c directions for a simple model of YBa2Cu3O7. In this model there are two layers---representing a CuO2 plane and a CuO chain---per unit cell. There is a BCS-like pairing (both s wave and d wave are considered) interaction localized in the CuO2 planes. The CuO chains become superconducting at temperatures lower than Tc because of their proximity to the planes, and there is an induced gap in the chains. Since the temperature dependence of the penetration depth in the b direction (along the chains) is sensitive to the size of the induced gap, the difference between the shapes of the penetration depth curves in the a and b directions reveals a great deal about the nature of the condensate in the chains. We find that in our proximity model there are always regions of the chain Fermi surface on which the induced gap is much smaller than Tc, so that the temperature dependence of λb is always different than that of λa. Experimental observations of the ab anisotropy show nearly identical temperature dependences. The main result of our paper, then, is that a simple proximity model in which the pairing interaction is localized to the planes and the planes are coherently coupled to the chains cannot account for the superfluid on the chains