Tunneling study of two-band superconductivity in MgB$_{2}$

Thin film Pb/barrier/MgB$_{2}$ sandwich-type tunnel junctions have been fabricated. The MgB$_{2}$ films were epitaxially grown on (211) MgO substrates with c-axis tilted by 19.5 degrees with respect to the substrate normal by hybrid physical-chemical vapor deposition. Tunneling from both $\sigma $ and $\pi $ bands of MgB$_{2}$ to Pb is observed from the current-voltage characteristics (CVCs). The temperature dependence and the magnetic field dependence of the two gaps were obtained by fitting the CVCs in the framework of two band superconductivity. It shows that at zero temperature and zero field, $\Delta _{\sigma } \quad \approx $ 2.3 mV and $\Delta _{\pi } \quad \approx $ 7.4 mV. As the applied magnetic field normal to the substrate increases, the contribution from the $\pi $ gap is suppressed much more quickly than the $\sigma $ gap, which is in agreement with lower critical field corresponding to the $\pi $ gap.