Structural phases of elemental Ga: Universal relations in conventional superconductors

The temperature dependent measurements of the thermodynamic critical field and the specific heat for the pressure stabilized Ga-II phase of elemental gallium are presented. The discussion of these and other Ga phases data in the context of elemental and binary phonon-mediated superconductors allowed to establish simple scaling relations between BCS quantities such as ${B}_{\mathrm{c}}(0)/{T}_{\mathrm{c}}\sqrt{{\ensuremath{\gamma}}_{\mathrm{e}}}$ and the specific heat jump at ${T}_{\mathrm{c}}$ versus the coupling strength $2\mathrm{\ensuremath{\Delta}}/{k}_{\mathrm{B}}{T}_{\mathrm{c}}$ [$\mathrm{\ensuremath{\Delta}}$ and ${B}_{\mathrm{c}}(0)$ are the zero-temperature values of the superconducting energy gap and the thermodynamic critical field, respectively, ${T}_{\mathrm{c}}$ is the transition temperature, and ${\ensuremath{\gamma}}_{\mathrm{e}}$ is the electronic specific heat]. The scaling relations can be analytically expressed by taking into account strong-coupling corrections to BCS theory. Such correlations can naturally explain the linear relation between ${B}_{\mathrm{c}}(0)$ and ${T}_{\mathrm{c}}$, which holds for conventional superconducting materials.