Pressure weakens coupling strength in In and Sn elemental superconductors

Abstract

Pressure dependence of the thermodynamic critical field $B_{\rm c}$ in elemental indium (In) and tin (Sn) superconductors was studied by means of the muon-spin rotation/relaxation. Pressure enhances the deviation of $B_{\rm c}(T)$ from the parabolic behavior, expected for a typical type-I superconductor, suggesting a weakening of the coupling strengths $\alpha=\langle\Delta\rangle /k_{\rm B}T_{\rm c}$ ($\langle\Delta\rangle$ is the average value of the superconducting energy gap, $T_{\rm c}$ is the transition temperature and $k_{\rm B}$ is the Boltzmann constant). As pressure increases from 0.0 to $\simeq 3.0$ GPa $\alpha$ decreases linearly, by approaching the limiting weak-coupling BCS value $\alpha_{\rm BCS}=1.764$. Analysis of the data within the framework of the Eliashberg theory reveals that only part of the pressure effect on $\alpha$ can be attributed to the effect of hardening of the phonon spectra, which is reflected by a decrease of the electron-phonon coupling constant. Nearly 40% of the effect is caused by increased anisotropy of the superconducting energy gap.