Isotropic single gap superconductivity of elemental Pb: the `smiling' approach

The unconventional multi-gap superconductivity in elemental Pb were reported previously by surface sensitive tunneling experiments, as well as predicted by several theory works. To obtain bulk evidence for such multiple gap behavior, the thermodynamic critical field $B_{\rm c}$ was measured along three different crystallographic directions ([100], [110], and [111]) in a high-quality Pb single crystal by means of muon spin rotation/relaxation. No difference in temperature evolution of $B_{\rm c}$ for all three directions was detected. The average reduced gap $\alpha=\Delta/k_{\rm B}T_{\rm c}=2.312(3)$ ($\Delta$ is the zero-temperature gap value and $T_{\rm c}$ is the transition temperature) was further obtained by employing the phenomenological $\alpha-$model. Our results imply that the elemental Pb is an isotropic superconductor with a single energy gap.
Comment: 6 pages, 3 figures. The version without `smiling' description to appear in Physical Review B as a Letter