Year: 2013
Type: article
Abstract: 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 $|d\ensuremath{\rho}/d\ensuremath{\theta}|$ of the normalized superfluid density $\ensuremath{\rho}={\ensuremath{\lambda}}^{2}(0)/{\ensuremath{\lambda}}^{2}(\ensuremath{\theta})$ at the transition $\ensuremath{\theta}=T/{T}_{c}=1$ has a minimum near the value of the pair-breaking parameter separating gapped and gapless states. The low-$T$ exponentially flat part of $\ensuremath{\rho}$ for the $s$-wave materials is suppressed by increasing pair breaking. For strong ${T}_{c}$ suppression by magnetic impurities the ``Homes scaling'' ${\ensuremath{\lambda}}^{\ensuremath{-}2}(0)\ensuremath{\propto}\ensuremath{\sigma}{T}_{c}$ with $\ensuremath{\sigma}$ being the normal conductivity gives way to ${\ensuremath{\lambda}}^{\ensuremath{-}2}(0)\ensuremath{\propto}\ensuremath{\sigma}{T}_{c}^{2}$. 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 $\ensuremath{\rho}$ 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, $\ensuremath{\rho}(\ensuremath{\theta})$ is only weakly dependent on the scattering parameter, i.e., it is nearly universal.
Source: Physical Review B
Authors: V. G. Kogan, R. Prozorov, V. Mishra
Language: English
Subfield: Condensed Matter Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1979649352