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 $\lambda(T,B)$ and the superfluid density $\rho_s(T)$ using a tunnel-diode-oscillator (TDO)-based method and by transverse field muon-spin rotation ($\mu$SR) spectroscopy. $\lambda(T)$ follows an exponential-type temperature dependence at $T\ll T_{c}$, but its zero-temperature value $\lambda(0)$ increases linearly with magnetic field. Detailed analyses demonstrate that both $\lambda(T)$ and the corresponding $\rho_{s}(T)$, measured in the Meissner state by the TDO method are well described by a two-gap $\gamma$ model with gap sizes of $\Delta_1(0)=1.31k_{B}T_c$ and $\Delta_2(0)=1.80k_{B}T_c$ and a very weak interband coupling. In contrast, $\rho_s(T)$, derived from the $\mu \rm{SR}$ data taken in a small field, can be fitted by a single-gap BCS model with a gap close to $\Delta_2(0)$. We conclude that LaPt$_{4}$Ge$_{12}$ is a marginal two-gap superconductor and the small gap $\Delta_1$ 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.