London penetration depth and pair breaking

The London penetration depth is evaluated for isotropic materials for any transport and pair-breaking Born scattering rates. Besides known results, a number of features are found. The slope vertical bar d rho/d theta vertical bar of the normalized superfluid density rho = lambda(2)(0)/lambda(2)(theta) at the transition theta = T/T-c = 1 has a minimum near the value of the pair-breaking parameter separating gapped and gapless states. The low-T exponentially flat part of rho for the s-wave materials is suppressed by increasing pair breaking. For strong T-c suppression by magnetic impurities the Homes scaling lambda(-2)(0) proportional to sigma T-c with sigma being the normal conductivity gives way to lambda(-2)(0) proportional to sigma T-c(2). For the d-wave order parameter, the transport and spin-flip Born scattering rates enter the theory only as a sum; in particular, they affect the T-c depression in the same manner. We confirm that the linear low-temperature behavior of rho in a broad range of the combined scattering parameter turns to the T-2 behavior only when the critical temperature is suppressed at least by a factor of 3 relative to the clean limit T-c0. Moreover, in this range, rho(theta) is only weakly dependent on the scattering parameter, i.e., it is nearly universal.