Systematic study of two-band/two-gap superconductivity in carbon-substituted ${\mathrm{MgB}}_2$ by point-contact spectroscopy

Point-contact measurements on the carbon-substituted $\mathrm{Mg}{\left({\mathrm{B}}_{1-x}{\mathrm{C}}_x\right)}_2$ filament/powder samples directly reveal a retention of the two superconducting energy gaps in the whole doping range from $x=0$ to $x\approx 0.1$. The large gap on the $\sigma$-band is decreased in an essentially linear fashion with increasing the carbon concentrations. The changes in the small gap ${\Delta }_{\pi }$ up to 3.8% $\mathrm{C}$ are proportionally smaller and are more difficult to detect but for the heavily doped sample with $x\approx 0.1$ and $T_c=22\mathrm{K}$ both gaps are still present, and significantly reduced, consistent with a strong essentially linear, reduction of each gap with the transition temperature.

Figure 1

Full lines, $\mathrm{Mg}{\left({\mathrm{B}}_{1-x}{\mathrm{C}}_x\right)}_2$ point-contact spectra at $T=4.2\mathrm{K}$ (except for the top spectrum recorded at 1.6 K). Open circles, fitting for the thermally smeared BTK model for two gaps. The fitting parameters, for the pure ${\mathrm{MgB}}_2$, ${\Delta }_{\pi }=2.3\mathrm{meV}$, ${\Gamma }_{\pi }=0.4\mathrm{meV}$, ${\Delta }_{\sigma }=6.6\mathrm{meV}$, ${\Gamma }_{\sigma }=0.05\mathrm{meV}$, $\alpha =0.78$; for the $x=0.021\mathrm{C}$ concentration, ${\Delta }_{\pi }=2.4\mathrm{meV}$, ${\Gamma }_{\pi }=0.4\mathrm{meV}$, ${\Delta }_{\sigma }=6.55\mathrm{meV}$, ${\Gamma }_{\sigma }=0.38\mathrm{meV}$, $\alpha =0.8$; for the $x=0.038\mathrm{C}$ concentration, ${\Delta }_{\pi }=2.3\mathrm{meV}$, ${\Gamma }_{\pi }=0.18\mathrm{meV}$, ${\Delta }_{\sigma }=6.1\mathrm{meV}$, ${\Gamma }_{\sigma }=0.3\mathrm{meV}$, $\alpha =0.78$ and for the $x=0.1$ C concentration ${\Delta }_{\pi }=1.65\mathrm{meV}$, ${\Gamma }_{\pi }=0.34\mathrm{meV}$, ${\Delta }_{\sigma }=3.2\mathrm{meV}$, ${\Gamma }_{\sigma }=0.55\mathrm{meV}$, $\alpha =0.75$. The $z$-parameter scattered between 0.44 and 0.65. Open triangles for $x=0.1$ curve, fit to the one-gap BTK formula. The upper curves are vertically shifted for the clarity. The arrows indicate a development of the gaps with increasing carbon content.

Figure 2

$\mathrm{Mg}{\left({\mathrm{B}}_{0.9}{\mathrm{C}}_{0.1}\right)}_2$-Cu point-contact spectrum at $1.6\mathrm{K}$ (shown in Fig. 1) recorded at different magnetic fields. Partial suppression of the small gap contribution helps in revealing the large gap (see the text). The curves at finite fields are shifted down for clarity.

Figure 3

Distribution of the superconducting energy gaps of $\mathrm{Mg}{\left({\mathrm{B}}_{1-x}{\mathrm{C}}_x\right)}_2$ as obtained from numerous point-contact junctions on different samples of the particular $\mathrm{C}$ concentration. Asterisks, the gaps obtained from analysis of the specific heat (Ref. 14).

Figure 4

Superconducting energy gaps from point-contact experiments at lowest temperature as a function of $T_c$. The points, average energy of the particular gap distribution shown in Fig. 3. The error bars, the standard deviations in the distributions. Asterisks, deduced from analysis of the specific heat measurement (see the text). Lines are a guide for the eye.

Figure 5

Temperature dependence of the energy gaps of $\mathrm{Mg}{\left({\mathrm{B}}_{1-x}{\mathrm{C}}_x\right)}_2$ determined from the fitting of the point-contact spectra. Full lines represent the BCS prediction scaled to the $\pi$ and $\sigma$ gaps.