Evidence for One-Gap Superconductivity in Mg(B$_{1-x}$C$_{x})_{2}$ Single Crystals at x=0.132 by Point-Contact Spectroscopy

Abstract

We report the results of directional point-contact measurements in Mg(B$_{1-x}$C$_{x})_{2}$ single crystals. The amplitudes of the gaps, $\Delta_{\pi}$ and $\Delta_{\sigma}$, were determined for each C content by fitting the experimental low-temperature normalized conductance curves of our “soft” point contacts with the BTK model generalized to the two-band case. We found that, on increasing the carbon content, $\Delta_{\sigma}$ decreases almost linearly with $T_{c}$ and $\Delta_{\pi}$ slightly increases until, at $x=0.132$ (where $T_{c}=19$ K), they assume the same value $\Delta =3.2 \pm 0.9$ meV. This result is confirmed by the temperature and magnetic-field dependence of the conductance curves at this C content, which do not show any evidence of two distinct gap values. In particular, the Δ versus T curve follows very well a standard BCS curve, with a gap ratio $2\Delta /k_{B} T_{c}=3.9$. These experimental findings are compared to the theoretical predictions of the two-band model in the Eliashberg formulation.