Reflection of a two-gap nature in penetration-depth measurements of MgB₂ film

The magnetic penetration depth λ(T) in the basal plane of a magnesium diboride (MgB₂) film was measured using a two-coil mutual-inductance technique at 50 kHz. This film has T_c≃38 K, ΔT_c<~1 K, and λ(0)∼1500±100 Å. At low temperatures, λ^-2(T) shows a clear exponential temperature dependence, indicating s-wave superconducting order-parameter symmetry. However, the data are not quantitatively well described by the theory assuming a single gap. From the data fitted by the full BCS calculation assuming a double gap, the values of the two distinct gaps were obtained: Δ_S(0)=2.61±0.41 meV and Δ_L(0)=6.50±0.33 meV. The contributions of the small and large gaps to the total superfluid density at T=0 were estimated to be 21% and 79%, respectively. Finally, we investigate how the penetration depth λ(T) is affected by the gap-size distribution on the Fermi surface.