Thermodynamic evidence for a pressure-driven crossover from strong- to weak-coupling superconductivity in Pb

The thermodynamic critical field $B_{\mathrm{c}}$ provides direct access to the superconducting condensation energy, yet its pressure dependence has been studied much less extensively than that of the transition temperature. Here, muon-spin-rotation/relaxation measurements of the thermodynamic critical field $B_{\mathrm{c}}$ of elemental Pb under hydrostatic pressure up to $\simeq 2.3$ GPa are reported. From the magnetic-field distribution in the intermediate state, $B_{\mathrm{c}}(T)$ is determined and $B_{\mathrm{c}}(0)$ is extracted at different pressures. In combination with previously reported high-pressure data for $B_{\mathrm{c}}$ and $T_{\mathrm{c}}$, it is shown that the pressure dependence of $B_{\mathrm{c}}(0)$ follows that of the superconducting gap $\mathrm{\Delta }(0)$ more closely than that of the transition temperature $T_{\mathrm{c}}$. At higher pressures, the logarithmic pressure derivatives of $B_{\mathrm{c}}(0)$ and $T_{\mathrm{c}}$ are found to converge, indicating that the coupling strengths ratio $\alpha =\mathrm{\Delta }(0)\mathrm{/}{k}_{\mathrm{B}}{T}_{\mathrm{c}}$ becomes nearly pressure independent. This behavior is interpreted as thermodynamic evidence for a pressure-driven crossover from strong- to weak-coupling superconductivity in Pb.