Effect of strong scattering on the low-temperature penetration depth of a d-wave superconductor

For a pure superconductor in a d-wave-like state at temperatures T well below the critical temperature T_c, the deviation Δλ of the penetration depth from its zero-temperature value λ(0) is proportional to T. When the concentration n_i of strongly scattering impurities is nonzero, Δλ∝Tⁿ, where n=2 for T<T^*≪T_c and n=1 for T^*<T≪T_c. The crossover temperature T^* and the increase in λ(0) scale as √n_i up to logarithmic corrections when resonant scattering is dominant. We argue that this case is relevant to recent measurements on YBa₂Cu₃O_7-δ and present specific results for a model pairing state with d_x²-y² symmetry.