Thermodynamic Evidence for Pressure-Driven Evolution towards Weak-Coupling Superconductivity in Pb

The thermodynamic critical field B_{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_{c} of elemental Pb under hydrostatic pressure up to ≃2.3  GPa are reported. From the magnetic-field distribution in the intermediate state, B_{c}(T) is determined and B_{c}(0) is extracted at different pressures, thereby providing direct thermodynamic access to the pressure evolution of the condensation-energy scale. It is shown that, within the experimentally accessible pressure range, the pressure dependence of B_{c}(0) follows that of the superconducting gap Δ(0) more closely than that of the transition temperature T_{c}. The measured pressure derivative of the coupling ratio α=Δ(0)/(k_{B}T_{c}) is furthermore found to agree with the difference between the pressure derivatives of B_{c}(0) and T_{c}, providing a direct thermodynamic confirmation of the relation between these quantities. Together, these results show that pressure suppresses strong-coupling effects in Pb. When viewed together with previously reported high-pressure data for B_{c} and T_{c}, the present results indicate that this tendency continues toward a regime in which α becomes nearly pressure independent.