Simple Model for the Variation of Superfluid Density with Zn Concentration in YBCO

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 $\pi {\xi }_{ab}^2$ 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 with x at temperature T = 0, using both a numerical approach and an analytical approximation. For $\delta =0.37$, if we use the value ${\xi }_{ab}$ = 18.3 angstrom, 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 ${\xi }_{ab}$, whose value is not widely agreed upon. The model also predicts a peak in the real part of the conductivity, Re${\sigma }_e(\omega ,x)$, at concentrations $x\sim x_c$, and low frequencies, and a variation of critical current density with x of the form $J_c(x)\propto n_{S,e}(x{)}^{7/4}$ near percolation, where $n_{S,e}(x)$ is the in-plane superfluid density.

19 pages including 6 figures, submitted to Physica C

References in corpus (2)

• Nodal Quasiparticle Lifetime in the Superconducting State of BSCCO(2212)
• What can we learn from comparison between cuprates and He films ? : phase separation and fluctuating superfluidity

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