Magnetic susceptibility and superfluid density of inhomogeneous superconducting films: the Tc-mosaic model
Abstract
Whole-sample and mutual-inductance part-sample measurements of the linear magnetic susceptibility, χ, of superconducting films are routinely used to obtain the London penetration depth, λ(T), assuming uniform superconductivity. However, spatially resolved probes show that many films of current interest are inhomogeneous on micrometer scales. Here we ask whether a distribution of local transition temperatures in a fully gapped film can produce an apparent line-nodal, T-linear λ(T). The film is modeled as a random Voronoi mosaic of domains with Tc distributed between Tc,min and Tc,max with s-wave (also d-wave, for comparison) London response inside each domain. We show that detectable screening appears only below the percolation temperature, Tp, and the transition broadens with the spread of Tc. For s-wave domains, λ(T) remains activated for any Tc,min>0. Only for Tc,min=0 does it become a power law, Δλ∝ Tn with n≈1.7, but then the onset of screening drops to Tp=Tc,max/2. Weighting the Tc distribution towards Tc→0 (more low-Tc domains) can bring n closer to 1 (n≈1.2), but simultaneously pushes the apparent transition, Tp, more than an order of magnitude below Tc,max. For d-wave domains, the linear term survives, and its relative slope is enhanced almost fourfold for Tc,min=0. Hence, a T-linear λ(T) measured in a film with screening onset within a factor of a few of Tc,max by whole-sample or mutual-inductance part-sample measurements cannot originate from Tc mosaicity in a fully gapped superconductor.
Related
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BibTeX
@misc{prozorov2026magnetic,
title = {{Magnetic susceptibility and superfluid density of inhomogeneous superconducting films: the Tc-mosaic model}},
author = {Ruslan Prozorov},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34796},
eprint = {2610.34796},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34796},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Magnetic susceptibility and superfluid density of inhomogeneous superconducting films: the Tc-mosaic model
AU - Ruslan Prozorov
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.34796
UR - https://arxiv.org/abs/2610.34796
AB - Whole-sample and mutual-inductance part-sample measurements of the linear magnetic susceptibility, χ, of superconducting films are routinely used to obtain the London penetration depth, λ(T), assuming uniform superconductivity. However, spatially resolved probes show that many films of current interest are inhomogeneous on micrometer scales. Here we ask whether a distribution of local transition temperatures in a fully gapped film can produce an apparent line-nodal, T-linear λ(T). The film is modeled as a random Voronoi mosaic of domains with T_c distributed between T_c,min and T_c,max with s-wave (also d-wave, for comparison) London response inside each domain. We show that detectable screening appears only below the percolation temperature, T_p, and the transition broadens with the spread of T_c. For s-wave domains, λ(T) remains activated for any T_c,min>0. Only for T_c,min=0 does it become a power law, Δλ∝ T^n with n≈1.7, but then the onset of screening drops to T_p=T_c,max/2. Weighting the T_c distribution towards T_c→0 (more low-T_c domains) can bring n closer to 1 (n≈1.2), but simultaneously pushes the apparent transition, T_p, more than an order of magnitude below T_c,max. For d-wave domains, the linear term survives, and its relative slope is enhanced almost fourfold for T_c,min=0. Hence, a T-linear λ(T) measured in a film with screening onset within a factor of a few of T_c,max by whole-sample or mutual-inductance part-sample measurements cannot originate from T_c mosaicity in a fully gapped superconductor.
ER -