Simple Model for the Variation of Superfluid Density with Zn Concentration in YBa2Cu3O7−δ

We describe a simple model for calculating the zero-temperature superfluid density of Zn-doped YBa2Cu3O7−δ 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 CuO2 layer, in which a substitutional Zn impurity creates a normal region of area πξ2 ab around it as originally suggested by Nachumi et al. Here ξab 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 with x at temperature T = 0, using both a numerical approach and an analytical approximation. For δ = 0.37, if we use the value ξab = 18.3 Å, we find that the in-plane superfluid decreases with increasing x and vanishes near xc = 0.01 in the analytical approximation, and near xc = 0.014 in the numerical approach. xc is quite sensitive to ξab, whose value is not widely agreed upon. The model also predicts a peak in the real part of the conductivity, Reσe(ω, x), at concentrations x ∼ xc, and low frequencies, and a variation of critical current density with x of the form Jc(x) ∝ nS,e(x) 7/4 near percolation, where nS,e(x) is the in-plane superfluid density.