## Simple Model for the Variation of Superfluid Density with Zn
Concentration in YBa_2Cu_3O_(7-\delta)

#### J. D. Chai, S. V. Barabash, and D. Stroud
Department of Physics, The Ohio State University, Columbus,
Ohio 43210

We describe a simple model for calculation the zero-temperature superfluid
density of Zn-doped YBa_2Cu_3O_(7-\delta) as a function of the fraction x
of in-plane Cu atoms which are replaced by Zn. The basis of the calculation is
a ``Swiss-cheese'' picture of a single CuO_2 layer, in which a substitutional
Zn impurity creates a normal region of area \pi\xi_(ab)^2 around it as
originally suggested by Nachumi et al. Here \xi_(ab) is the zero-temperature
in-plane coherence length at x = 0. We use this picture to calculate the
variation of the in-plane superfluid density at temperature T = 0, using
both a numerical approach and an analytical approximation. For \delta = 0.37,
if we use the value \xi_(ab) = 37 Angstroms, we find that the in-plane
superfluid density decreases with increasing x and vanishes near x_c = 0.01
in the analytical approximation and near x_c = 0.014 in the numerical
approach. x_c is quite sensitive to \xi_(ab), whose value is not widely
agreed upon. The model also predicts a peak in the real part of the
conductivity sigma(omega, x) at concentrations x = x_c and low frequencies,
and a variation of critical current density with x of the form
J_c(x) ~ n_(S,e)(x)^(1.75), near percolation, where n_(S,e)(x) is the
in-plane superfluid density.