Conductance Measurements of Magnesium Diboride-based Josephson Junctions Below 1 Kelvin: Beyond the 2-Gap Model

Theoretical and experimental studies have probed the nature of magnesium diboride's two superconducting energy gaps $\Delta_\pi$ and $\Delta_\sigma$. Several theoretical analyses have predicted fine structures within each energy gap, with recent experiments revealing similar structures. We have performed high-resolution tunneling measurements of low-transparency Josephson junctions using ``terraced,'' ``columnar,'' and c-axis MgB$_2$ films separated by its native oxide from either lead (Pb) or tin (Sn) counter-electrodes. Using high-resolution I-V data at $T$ as low as 23mK, we observe sub-structures within both energy gaps. We also observe sharp peaks in the subgap that identify, to high precision, the energy gap values of the junction counter-electrodes (Pb and Sn). These lead us to conclude that the substructures seen in the gaps are due to MgB$_2$. We then fit the data using simplified two-gap and four-gap models with variable weights and broadening factors. By demonstrating the inadequacy of a simple two-gap model in fitting the data, we illustrate that some distinctions between theoretical models of energy gap substructures are experimentally observable.