Simple model for the variation of superfluid density with Zn concentration in YBa 2Cu 3O 7− δ

Abstract

We describe a simple model for calculating the zero-temperature superfluid density of Zn-doped YBa 2Cu 3O 7− 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 CuO 2 layer, in which a substitutional Zn impurity creates a normal region of area π ξ ab 2 around it as originally suggested by Nachumi et al. Here ξ 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 with x at temperature T=0, using both a numerical approach and an analytical approximation. For δ=0.37, if we use the value ξ ab =18.3 Å, we find that the in-plane superfluid 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 ξ ab , whose value is not widely agreed upon. The model also predicts a peak in the real part of the conductivity, Re σ e ( ω, 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) 7/4 near percolation, where n S, e ( x) is the in-plane superfluid density.