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

TL;DR

This study provides bulk evidence that elemental lead (Pb) exhibits isotropic single-gap superconductivity, contradicting previous surface-sensitive reports of multi-gap behavior, through measurements of the thermodynamic critical field in different crystallographic directions.

Contribution

The paper presents the first bulk thermodynamic evidence that elemental Pb is an isotropic superconductor with a single energy gap, challenging prior surface-sensitive multi-gap findings.

Findings

No directional dependence in critical field $B_c$ temperature evolution.

Average reduced gap $eta=2.312$ consistent with single-gap superconductivity.

Bulk measurements support isotropic single-gap behavior of Pb.

Abstract

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.