Point-contact spectroscopy of Al- and C-doped $\mathrm{Mg}{\mathrm{B}}_2$: Superconducting energy gaps and scattering studies

The two-band and/or two-gap superconductivity in aluminum- and carbon-doped $\mathrm{Mg}{\mathrm{B}}_2$ has been addressed by the point-contact spectroscopy. Two gaps are preserved in all samples with $T_c^{\prime }s$ down to $22\mathrm{K}$. The evolution of two gaps as a function of the critical temperature in the doped systems suggests the dominance of the band-filling effects, but for the increased Al doping, the enhanced interband scattering must also be considered. The extraction of the zero-energy density of states for the $\pi$ and $\sigma$ bands using a simple physical model demonstrates that significant changes in the relative weighting of the intraband scattering are created in the case of the C doping with the scattering in the $\pi$ band enhanced faster than in the $\sigma$ one. The Al doping does not change the relative weight of the scatterings within the bands.

Figure 1

Influence of the applied magnetic field on the representative point-contact spectra of ${\mathrm{Mg}}_{1-x}{\mathrm{Al}}_x{\mathrm{B}}_2$ samples measured at indicated temperatures (solid lines). Open circles show the fitting curves for the two-gap BTK model in zero and finite magnetic fields.

Figure 2

Influence of the applied magnetic field on the representative point-contact spectra of $\mathrm{Mg}{\left({\mathrm{B}}_{(1-y)}{\mathrm{C}}_y\right)}_2$ samples measured at indicated temperatures (solid lines). Open circles show the fitting curves for the two-gap BTK model in zero and finite magnetic fields.

Figure 3

Distribution of the superconducting energy gaps of $\mathrm{Mg}{\left({\mathrm{B}}_{(1-y)}{\mathrm{C}}_y\right)}_2$ (gray columns) and ${\mathrm{Mg}}_{1-x}{\mathrm{Al}}_x{\mathrm{B}}_2$ (open columns). The dashed and dotted lines are guides for the eyes.

Figure 4

Averaged values of the superconducting energy gaps as a function of the critical temperatures of $\mathrm{Mg}{\left({\mathrm{B}}_{(1-y)}{\mathrm{C}}_y\right)}_2$ (solid circles) and ${\mathrm{Mg}}_{1-x}{\mathrm{Al}}_x{\mathrm{B}}_2$ samples (open squares). The error bars represent the standard deviations in the distribution shown in Fig. 3. For the lines, see text.

Figure 5

(a) Zero-energy DOS $N_{\pi }(0,h)$ of ${\mathrm{Mg}}_{1-x}{\mathrm{Al}}_x{\mathrm{B}}_2$ determined from the fitting to the two-band mixed-state BTK formula. The applied field has been rescaled to the value of $H_{c2\Vert c}\approx 3\mathrm{T}$ (Ref. 18). (b) $N_{\pi }(0,h)$ of $\mathrm{Mg}{\left({\mathrm{B}}_{(1-y)}{\mathrm{C}}_y\right)}_2$. The applied field has been rescaled to $H_{c2\Vert c}\approx 5$, 8, and $8\mathrm{T}$. (Refs. 4, 39) The dashed and dotted lines represent the theoretical predictions of $N_{\pi }(0,h)$ (Ref. 32) for the dirty $\mathrm{Mg}{\mathrm{B}}_2$ samples with the ratios of in-plane diffusivities $D_{\sigma }∕D_{\pi }=0.2$ and 1, respectively. The solid lines are guides for the eyes.