Measurement and modeling of the low-temperature penetration-depth anomaly in high-quality MgB2 thin films

Based on our measurements of intermodulation distortion in MgB₂, we have previously proposed that the π energy-gap in MgB₂ entails six nodal lines [Y.D. Agassi, D.E. Oates, and B.H. Moeckly, Phys. Rev. B 80 (2009) 174522]. Here we report high-precision measurements in MgB₂ stripline resonators that show an increase of the penetration depth as the temperature is decreased below 5 K. This increase is consistent with the ℓ = 6 symmetry of the π energy gap that we have proposed. We interpret the increase as a manifestation of Andreev surface-attached states that are associated with the nodal lines of the π energy gap. Penetration-depth calculations are in good agreement with our data. To reconcile the present interpretation with existing literature, we review other penetration-depth data, magnetic-impurity and tunneling experiments, and data on the paramagnetic Meissner effect. We conclude that these data do not rule out the interpretation of our experimental data based on a nodal π energy gap.