Effect of Hydrostatic Pressure on Superconducting Lead-Indium Alloys Using Electron Tunneling

Abstract

The effect of pressure on the effective phonon spectrum ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})F(\ensuremath{\omega})$, the dimensionless electron-phonon interaction strength $\ensuremath{\lambda}$, and the average electron-phonon coupling function $〈{\ensuremath{\alpha}}^{2}〉$ has been determined in the superconducting alloys ${\mathrm{Pb}}_{95}$${\mathrm{In}}_{5}$ and ${\mathrm{Pb}}_{88}$${\mathrm{In}}_{12}$. Electron-tunneling measurements at pressures from 0 to 3600 bar provided the energy gap and tunneling density of states which served as input to McMillan's gap inversion program which calculated ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})F(\ensuremath{\omega})$, $\ensuremath{\lambda}$, and $〈{\ensuremath{\alpha}}^{2}〉$. Pressure production was via solid helium which provided nearly hydrostatic pressures. The energy gap decreases and the phonon frequencies increase with increasing pressure. The impurity band undergoes the smallest relative shift with increasing pressure and the transverse peak exhibits the largest relative shift. ${\ensuremath{\alpha}}^{2}(\ensuremath{\omega})F(\ensuremath{\omega})$ shifts toward higher frequencies and decreases slightly in amplitude. The net result of all these effects is for a shift of the electron-phonon interaction toward weaker coupling. The best indicators of this trend are the observed decrease of $\ensuremath{\lambda}$ and $〈{\ensuremath{\alpha}}^{2}〉$ with increasing pressure. These values are $\frac{d\mathrm{ln}\ensuremath{\lambda}}{\mathrm{dP}}=\ensuremath{-}7.9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{bar}}^{\ensuremath{-}1}$ and $\frac{d\mathrm{ln}〈{\ensuremath{\alpha}}^{2}〉}{\mathrm{dP}}=\ensuremath{-}3.2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ ${\mathrm{bar}}^{\ensuremath{-}1}$ for ${\mathrm{Pb}}_{88}$${\mathrm{In}}_{12}$. The values for ${\mathrm{Pb}}_{95}$${\mathrm{In}}_{5}$ are close to these. The pressure dependence of $\ensuremath{\gamma}$, the electronic-specific-heat coefficient, determined from the pressure dependence of the quanity ${Z}_{n}(0)=1+\ensuremath{\lambda}$, gives a value close to that of Pb determined from thermal-expansion measurements and from recent theoretical considerations.