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Weak Interband-Coupling Superconductivity in the Filled Skutterudite LaPt4Ge12

The superconducting pairing state of LaPt$_{4}$Ge$_{12}$ is studied by measuring the magnetic penetration depth $λ(T,B)$ and the superfluid density $ρ_s(T)$ using a tunnel-diode-oscillator (TDO)-based method and by transverse field muon-spin rotation ($μ$SR) spectroscopy. $λ(T)$ follows an exponential-type temperature dependence at $T\ll T_{c}$, but its zero-temperature value $λ(0)$ increases linearly with magnetic field. Detailed analyses demonstrate that both $λ(T)$ and the corresponding $ρ_{s}(T)$, measured in the Meissner state by the TDO method are well described by a two-gap $γ$ model with gap sizes of $Δ_1(0)=1.31k_{B}T_c$ and $Δ_2(0)=1.80k_{B}T_c$ and a very weak interband coupling. In contrast, $ρ_s(T)$, derived from the $μ\rm{SR}$ data taken in a small field, can be fitted by a single-gap BCS model with a gap close to $Δ_2(0)$. We conclude that LaPt$_{4}$Ge$_{12}$ is a marginal two-gap superconductor and the small gap $Δ_1$ seems to be destroyed by a small magnetic field. In comparison, in PrPt$_4$Ge$_{12}$ the $4f$-electrons may enhance the interband coupling and, therefore, give rise to more robust multiband superconductivity.