Effects of He$^{+}$ ion irradiation on the two-band superconductivity of MgB$_{2}$ by point-contact spectroscopy

An unresolved issue in MgB$_{2}$ is whether the two superconducting gaps can be merged into a single gap as T$_{c}$ is reduced. It has been predicted that several effects, including enhanced interband scattering or a smeared density of states, can reduce T$_{c}$. Our transport measurements on MgB$_{2}$ thin films un-irradiated and irradiated with 1 MeV He$^{+}$ ions (doses: 1x10$^{15}$ -- 1x10$^{17}$ ions/cm$^{2})$ show that $\rho _{40K}$ increases and that T$_{c}$ decreases roughly linearly with dose and $\rho _{40K}$, similar to other work [R. Gandikota \textit{et al}., cont-mat/0410655]. Point-contact spectroscopy on MgB$_{2}$ irradiated with 1x10$^{16}$ ions/cm$^{2}$, with T$_{c}$ reduced to 36.3 K from 39.3 K, shows that 2$\Delta $/k$_{B}$T$_{c}$ increases from 1.43 to 1.76 (decreases from 4.13 to 3.90) for the smaller (larger) gap, so the gaps tend to merge. Detailed measurements and analyses based on the existing models [$e.g.$, J. M. Rowell, SST \textbf{16} R17 (2003), and J. Kortus \textit{et al}., cond-mat/0411667] will be presented. We acknowledge Pavel Krasnochtchekov and Robert Averback and support by the DoE DEFG02-91ER45439, through the FSMRL and the Center for Microanalysis of Materials.