Calculation of the Effect of Random Superfluid Density on the Temperature Dependence of the Penetration Depth Page: 2 of 19
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I. INTRODUCTION
The penetration depth and its temperature dependence are important characteristics of
any superconductor and are considered key to determining the momentum space structure of
the order parameter.1-3 The possibility of disorder in exotic superconductors is well known,
but analyses performed to date have concentrated on the effect of disorder-induced scattering
on the momentum space structure of the gap.4-7 This paper is motivated by the possibility
that disorder may lead to nanoscale real space variation and the associated need to model
the relationship between such spatial variation and properties that are measured on longer
length scales. We address how inhomogeneity in the penetration depth may affect bulk
measurements of the penetration depth for methods that rely on Meissner screening and can
be analyzed by solutions to London's equation. In particular, we show that the measured
result is not simply given by the average value of the penetration depth, but is affected by
the statistical structure of the spatial variations in the penetration depth.
Many superconductors are created by chemical doping of a non-superconducting parent
compound. In these systems the inherent randomness of the doping process may give rise
to an inhomogeneous superconducting state. The importance of this effect will be deter-
mined by the characteristic length over which the dopant atoms affect the superconductivity.
Even in the most ordered material, there will be binomial fluctuations in the total number of
dopants in a given region. In general, one does not expect significant spatial variation in ma-
terials that are weakly correlated and can be described by a rigid band model. For example,
disorder is largely irrelevant in classic metallic superconductors, due to their long coherence
lengths and weakly correlated nature.8 In contrast, the cuprates are doped insulators with
a coherence length on the scale of the lattice. They are known to have nanoscale disorder
in their superconducting properties, as seen by scanning tunneling microscopy.9 Similar gap
maps have been observed in the iron pnictide family'-12 and in disordered titanium nitride
films close to the superconductor to insulator transition.1314
Materials with intrinsic disorder present two separate challenges. Understanding how the
random doping process gives rise to local superconducting properties, such as the penetration
depth or local density of states, requires a microscopic model. But even with such a model,
we still need to make the connection between the local superconducting properties and bulk
measurements. The manner in which local superconducting properties relate to the observed2
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Lippman, Thomas & Moler, Kathryn A. Calculation of the Effect of Random Superfluid Density on the Temperature Dependence of the Penetration Depth, article, July 20, 2012; United States. (https://digital.library.unt.edu/ark:/67531/metadc830737/m1/2/: accessed March 28, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.