Observation of the Crossover from Two-Gap to Single-Gap Superconductivity through Specific Heat Measurements in Neutron-Irradiated ${\mathrm{MgB}}_2$

We report specific heat measurements on neutron-irradiated ${\mathrm{MgB}}_2$ samples, for which the critical temperature is lowered to 8.7 K, but the superconducting transition remains extremely sharp, indicative of a defect structure extremely homogeneous. Our results evidence the presence of two superconducting gaps in the temperature range above 21 K, while single-gap superconductivity is well established as a bulk property, not associated with local disorder fluctuations, when $T_c$ decreases to 11 K.

Figure 1

$T_c$ versus $\rho (40)$ for the samples listed in Table  and Ref. [21]. The continuous line is a guide for the eye.

Figure 2

$c/T$ as a function of $T^2$ for the samples P0, P3.5, P3.7, and P6.

Figure 3

$c_{\mathrm{sc}}/\gamma T$ as a function of $t$ for the samples P0, P4, P5, and P6. The best fit curves are plotted as continuous lines. For the samples P4 and P5 the best fit curves obtained within the single-gap (gray line) and two-gap (black line) analyses are presented for comparison.

Figure 4

${\Delta }_{\sigma }(0)$ (empty symbols), ${\Delta }_{\pi }(0)$ (filled symbols), and $\Delta (0)$ (half-filled symbols) as a function of $T_c$. In the main figure data from this work (■) and Ref. 19 (◀). In the inset, data from this work (■), Ref. 19 (◀), Ref. 9 (▲), Ref. 16 (▶), Ref. 18 (◆), and the theoretical curves calculated in Ref. 7 in the case of only interband scattering (dotted line) and only reduced DOS (continuous line).