Superfluid density near the critical temperature in the presence of random planar defects

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 are responsible for the variation of $T_c$, 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.