The superfluid density near the superconducting transition is investigated in the presence of spatial inhomogeneity in the critical temperature. Disorder is accounted for by means of a random $T_c$ term in the conventional Ginzburg-Landau action for the superconducting order parameter. Focusing on the case where a low density of randomly distributed planar defects is responsible for the variation in $T_c$, we derive the lowest-order correction to the superfluid density in powers of the defect concentration. The correction is calculated assuming a broad Gaussian distribution for the strengths of the defect potentials. Our results are in a qualitative agreement with the superfluid density measurements in the underdoped regime of high-quality YBCO crystals by Broun and co-workers.

• Received 7 August 2008

DOI:https://doi.org/10.1103/PhysRevB.78.214508