Role of spin-orbit coupling in the physical properties of LaX3 ( X=In , P, Bi) superconductors

Abstract

We report a comprehensive and complementary study on structural, elastic, mechanical, electronic, phonon, and electron-phonon interaction properties of $\mathrm{La}{X}_{3}$ ($X$ = In, Pb, and Bi) using first-principles density functional calculations within the local density approximation with and without the spin-orbit coupling (SOC). The calculated lattice parameters for these intermetallic compounds with and without SOC are found to differ by less than $2%$ from their experimental values. The effect of SOC on the elastic, mechanical, electronic, phonon, and electron-phonon interaction properties is more profound for ${\mathrm{LaPb}}_{3}$ and ${\mathrm{LaBi}}_{3}$ containing heavier $X$ elements rather than ${\mathrm{LaIn}}_{3}$ containing lighter $X$ element. The inclusion of SOC considerably removes the degeneracies of some bands near the Fermi level and makes some phonon branches in ${\mathrm{LaPb}}_{3}$ and ${\mathrm{LaBi}}_{3}$ softer and increases the strength of dominant peaks in their Eliashberg spectral functions. Thus the SOC related enhancement of their electron-phonon coupling parameter values can be related to both a softening of their phonon dispersion curves and an increase in their electron-phonon coupling matrix elements. The superconducting transition temperature with SOC is computed to be 0.69 K for ${\mathrm{LaIn}}_{3}$, 4.23 K for ${\mathrm{LaPb}}_{3}$, and 6.87 K for ${\mathrm{LaBi}}_{3}$, which agree very well with the respective measured values of 0.70, 4.18, and 7.30 K.