Penetration depth, multiband superconductivity, and absence of muon-induced perturbation in superconducting PrOs$_{4}$Sb$_{12}$

Transverse-field muon spin rotation ($μ$SR) experiments in the heavy-fermion superconductor PrOs$_{4}$Sb$_{12}$ ($T_{c}=1.85$ K) suggest that the superconducting penetration depth $λ(T)$ is temperature-independent at low temperatures, consistent with a gapped quasiparticle excitation spectrum. In contrast, radiofrequency (rf) inductive measurements yield a stronger temperature dependence of $λ(T)$, indicative of point nodes in the gap. This discrepancy appears to be related to the multiband structure of PrOs$_{4}$Sb$_{12}$. Muon Knight shift measurements in PrOs$_{4}$Sb$_{12}$ suggest that the perturbing effect of the muon charge on the neighboring Pr$^{3+}$ crystalline electric field is negligibly small, and therefore is unlikely to cause the difference between the $μ$SR and rf results.

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